Transcript for:
Comprehensive MCAT Physics and Math Guide

hey everybody welcome back to the channel in this video I will share everything that you need to know for the MCAT physics and math sections I personally use these miles down review sheets to get 100 percentile on the MCAT when I took it a couple of years ago I'm now a third-year med student and this was one of the main sources of my content review throughout my studying I'm going to supplement this review with pictures from Google images and my own questions to make sure that you're understanding and following along um I hope you find this helpful and let's get started so first thing we want to review is uh vectors and scale so this this first page is kind of things that you want to know down cold because they're pretty important for the MCAT and also very fundamental things you need to know for the physics section so vectors are it's important to know the difference between vectors and scalers vectors are things that have both magnitude and Direction and scalers are just things that have are quantities but not necessarily or don't have a direction and so the most important distinction here is the one between velocity and speed that's going to be tested um in in one way or the other but basically you want to know that something like velocity or acceleration or Force these are all numbers that are attached to directions um so I can't just tell you that the person's velocity was 5 mil hour I have to tell you that this person's velocity was 5 m hour going in the west direction if I just tell you that it's 5 miles hour then that's just their speed and so it's important to know that displacement velocity acceleration and force are all vectors and speed or coefficients of friction anything that's kind of a number is always going to be um is always going to be of scaler so vector addition is pretty important um they're not necessarily going to ask you um to add up vectors but it is kind of important to understand how it happens and so what happens is that you take um these these vectors so let's say the vector a and the vector B in this image and let's see so this is a and this is B and whenever you add up vectors you have to add up the the point of one with the tail of the other and so when I say a plus b then it's important to know that okay we start with a A is pointing this direction and then we put the tail of B and then that gets added up and so the fun the final Vector is one that goes from the tail of a to the point of B so A to B um it's also important to know that when you're doing vector addition you can reverse this and you'll still get the same answer so if you start with b and then you add a to that right B plus a is going to be the same Vector as a plus b so that's kind of how you do vector addition now how do you do Vector subtraction Vector subtraction is kind of the same thing um basically when you're doing Vector subtraction you want to reverse the ones that's being subtracted and then you can add them so let's look at another example subtraction okay so um let's say a minus B right A minus B is going to be you take the one that's a and then you're doing minus B so you have to reverse B so I'm going to take the vector of B so I'm I'm just going to draw it over here so this is a right and then B if we were're going to do negative B then would actually look this way um so this is the negative B Vector right so you add a and you add negative B and you get a and then I'm going to add the tail of negative B and if you remember negative B points this way so it's going to be a and then negative B and we're adding those two and we get this vector which is the the vector that goes this way so uh that's one way to do it now it is kind of important to know that um this is not the same thing as B minus a because B minus a would be this plus this and so B minus a would actually be going in the opposite direction as a minus B okay I hope that makes sense let's move on so Vector multiplication there's actually two um two important Concepts here one is you do the dot product and the other one is you do the cross product the important distinction here is that a DOT product is you get a scalar quantity in a cross product you get the vector as a result so a DOT product is the magnitude of a times the magnitude of B time cosine of theta and you have to remember that Theta is the angle that A and B form a cross product is the magnitude of a * the magnitude of B times the sign of the angle but then you have to remember that this results in a new vector and this is always something that's confused so many people me included which is that you have to find the new Vector based on this thing called the right hand rule so let's start with the dot product real quick and then I'll go over the cross product so the dot product dot product vectors is like this so a DOT product you would take the magnitude of a so the magnitude of a is you find what is um what is the uh here let's find a equation for the magnitude okay so to find the magnitude of a vector you essentially take the X and then you take the Y of that vector and you square the two and you add them and you take the square root of that so it's like the Pythagorean theorem so you take the magnitude of a vector so in this case you would take magnitude of a and then you multiply it by the magnitude of B and then you would take the Theta that those two those two vectors form and so it's important to know that when you're making the angle between those two vectors this is also something that confuses people is you want to take the Tails of the two vectors and take that angle in between the two tails and so that's going to give you the the the dot product between two vectors now let's do the cross product which is a little bit more complicated just because just because you have to know the right hand rule for this one so this is a good example so let's take a and B so a is going this way and B is going this way now what I do is there's two ways to do this I like to take my full hand but some people like to do the three fingers and essentially you point your hand in the direction of the first Vector in the direction of a so you do the same thing essentially as what you were doing for the dot product so you do magnitude of a Time magnitude of B time the S of the Theta and Dot product was cosine of theta but here you're first figuring out that scalar component and now you're figuring out which direction does the vector point in for uh cross product so you point your hand in the direction of a and then you curl your hand towards the direction of B so in this example I'm not sure if you're going to be able to see it let's increase my screen so in this example if my a vector is going this way and then I'm curling my hand inside for the B Vector as you could see in that example then my thumb is pointing up and that's kind of how you figure out the the the direction in which your cross product um is for is going in all right um so in this example again you can see let's see if I can show you by drawing over it so this is Direction sorry this is the direction of a and then we curl our hand this way to get the direction of B so now our hand should have curled this way and then our thumb is telling us which direction that the the cross product Vector is pointing in so that's how you do that um let's do another example example just so that you have that down um prod Vector Direction so um let's do this so this is how you do the right hand rule which is let's say a is pointing in that direction in this direction and B is pointing in this direction so we curl our hand just like this guy is doing this way and the way that our thumb is pointing us up so the cross product vector is going to point up and now you can see in this example a and then the C the B Vector is this so the only way that you can curl your finger is by pointing downward to curl that way because you can't Point your finger upward for that so now you know that the cross product a and the cross product of B is going downward um again it is important to know that the cross the A and B Vector cross product that is not the same Vector as boss cross product a and they're they're they might try to trip you up on this i' I've seen some practice exams where they try to trick you up on that but it's important to know that those are actually the opposite vectors because a a cross product with B will be pointing upward in this example and a b cross product with a would be pointing downward it would be the same scalar quantity but it would be pointing downward so that's kind of an important concept to know all right so we finished vectors and scalers now it's the mechanical equilibrium and this is free body diagrams is kind of the things that you do in physics class in high school or college where you see like there's this box that's rolling downwards and um your physics teacher is asking you to figure out all the forces that are acting on it so usually it's going to be um this box and then you'll have like the force of gravity pointing down and you'll have friction that's going in the opposite direction as the movement and then you'll have um some normal force which is kind of the contact force in between those two objects and so a free body diagram is the is the representation of all the forces that are acting on some object now translational equilibrium is when this object has no net forces um acting on it so a net force is basically when you add up all those forces using vector addition then you get the net force and so there's no net forces acting on an object now this is an important point where they'll try to trip you up which is um if there's no net forces on an object does that mean that that object is not moving I'll give you a second um so the answer to that is not necessarily because no net forces on an object means there's no acceleration on that object as we'll learn when we get the second law of Newton but um an object can be going at the same speed with zero acceleration like it can be going at 5 mph uh without stopping or without accelerating and that would have no net forces acting on it uh it could also be going at 0o Miles hour and just consistently just stay stationary and that would also have no net forces on it um okay rotational equilibrium so you can imagine like a a bowling ball and normally a bowling ball is rotating and um there's like somebody who's applying a net uh torque to that who's applying a force to that and that's causing a torque which causing this bowling ball to rotate um but if this bowling ball is has no net torque on it then that means that essentially there's no there's no um it's not ex it's not rolling any faster or slower than usual it's just kind of either uh rolling in a constant way or it's just not rolling at all and so that would be a rotational equilibrium um and then it's important to know that the center of mass is the most commonly use pivot point for something that has rotational equilibrium all right displacement and velocity now it's important to know and we kind of already talked about this which is the displacement is the change in position and its path independent um distance is that scalar quantity which reflects the path traveled and velocity represents the change in the displacement with respect to time so it's kind of important to know the differences between all of these and so let's say that I uh walk from my house to your house and then I walk back to my house right my displacement is zero um because I haven't actually throughout that entire time I ended up at the same spot my speed or my dist sorry my distance is actually that plus that um so it's whatever my walk is to U * 2 um so that's the distance and my displacement is zero because cuz I haven't moved at all so my velocity here would be zero my speed would be whatever the distance is divided by the total amount of time so that's kind of the difference between displacement and distance um velocity is the change in displacement with respect to time so it's important to know kind of the difference between that instantaneous velocity is the change in displacement over time as the time approaches zero and this is kind of where you get into a little bit of calculus which is that um if I'm like let's say my um uh I'm trying to think of the best let's say I'm running a marathon and at uh certain points in the marathon I'm running at like 5 mes hour and then 4 mil hour and then 3 mil hour and then 7 miles hour so like the ve the instantaneous velocity is the velocity that I'm moving at at this exact point in time and then the instantaneous speed is the magnitude of that velocity vector and so the change in displacement again versus the change in distance all right um now it's force and acceleration and this is absolutely absolutely fundamental for the mccat so the force is any push or pull on an object that results in acceleration um so my dad has this story that he tells me which is that uh his physics teacher once asked him to push a wall for five minutes and then he asked them did you do any force and the answer is actually no because it didn't result in any acceleration on that wall and so a push or pull that results in acceleration okay gravity is um the attractive force between two objects so most people think gravity is just the downward force on something um but the reason why that is a downward force is because essentially this is you and this is you standing on the earth and so you're you the Earth is putting a force on you right this is the earth the earth this is the gravitational force towards the Earth and then this is your Force towards the uh this is your this is your you are attracting the Earth and the Earth is attracting you it's just that the Earth has so much more mass that that results in a gravitational force for pulling you down but you're technically also pulling the force up pulling the Earth up a little bit it's just you're so tiny compared to the earth that the gravitational attractive force between you and the Earth is so tiny in in comparison um so friction is the force that opposes motion as a function of electrostatic interactions at the surfaces between two objects and so there's static friction which is when an object is not moving and kinetic friction which is when an object is moving and that's equal to the normal force times a coefficient and this coefficient is dependent on what uh surface you're looking at and so ice has a different kinetic friction or static friction as compared to like the chalk board you know and so it's important you don't need to know like different coefficients but you do know need to know that the normal force times that coefficient is equal to that friction it's also important to know that um this coefficient is going to be different based on static or kinetic friction um so you need to know whether the object is sliding or whether it's St to figure out what that force is all right um at this point it's probably important to know what normal force is so I I did mention it before but a normal force is essentially the contact between two objects and so let's say this is um a a slide and this is a box the normal force is going in this direction because it's the it's the the contact force between those so if I'm if I'm drawing the normal force on this box that this ramp exerts on this box it would be going this way uh and then it would also have a gravitational force pointing this way so this is the normal force all right um a measure of inertia on an object is the mass and so I was always I remember in third grade we were learning about masses versus weight and I would have no idea what either of that meant um mass is essentially how much uh stuff is in a material um and it's an inertia is kind of like how hard it is to move and so Mass doesn't change based on the gravitational force it's just kind of like how how much stuffff is in it uh weight does does change based on the grav based on the force that's um being placed on it and so how we measure weight is usually the gravitational attraction that that thing has to the Earth and so weight is definitely dependent on mass so like if you have more mass and you have more weight um but the idea is that if you go to a different planet and the gravitational attraction is a different constant then the weight is going to change but the mass stays the same because the mass is only dependent on the inertia of the object which is essentially how much stuff is in that object all right acceleration is the vector that represents the change in velocity over time and so if you were wondering why was I talking about um uh this thing instantaneous velocity before it's because we use that calculation of what the instantaneous velocity is and we figure out like how is that instantaneous velocity changing over time and that's what the acceleration is and then there's torque torque is you know mentioned it um over here in rotational equilibrium but torque is basically a twisting force that causes rotation and so um if I was going to draw let's say this is a a bowling ball right uh or this is just any ball so if I apply a force that's right up here then that's going to cause this ball to roll but if I applied a force like um if I applied a force like this to the ball at this point that that ball is not going to roll it'll um it won't roll because I'm not applying a force that causes twisting or causes torque and so important to know this is this is always confusing people but what are these two things so the the first uh coefficient is the distance from the center of mass that you're applying that force and so in both cases my distance was the radius because it's basically I'm applying it at this point which is at the very tip from here right so in this case this for this example would be my radius it could also be that I'm applying a force like right here for a ball and then in that case it would be um my radius from the force would be a little bit tinier so I'm just going to draw this out basically what you're looking at is this is a bowling ball and if I'm applying a force that goes this way then this is my Force vector and this is my R vector and this is Theta and remember when I mentioned that to calculate Theta you want to take the Tails of both so this is one vector this is the other vector and so Theta is going to be a 90° angle s of theta is just one and so it's going to be basically in this example the torque is going to be just this the radius times the force and we're going to get this scalar quantity that represents the um the product of those two all right um so that's kind of the torque and then it's important to also know what is um the final thing I want to mention about torque is that um this is going to be a vector um that is the the cross product of R and F and so you need to use the right hand rule to figure out where is the direction in which the torque is going all right Newton's Laws so these are pretty high yield too they're not going to ask you like what is Newton's law first one but it is important to know these things to figure out answers to physics questions so the first one is uh ma equals uh the net forces on something and that's where free body diagrams are really valuable um because um because you're going to be figuring out like what are all these forces that are acting on something you're going to add the vector vectors of the forces that are acting on something and then you're going to figure out okay based on this equation f equals ma what is the mass of the object what is the acceleration and what is the net force and it's important to know that if something is zero and I mentioned that when I was talking about translation equilibrium if the net forces of something is zero that means that that object is either at rest or at constant velocity it means that there's zero acceleration remember acceleration is the change in velocity over time the second law is that any acceleration is the result of a net force that's greater than zero which essentially is fnet equals Ma and so this means that if there's a force acting on something if there's a net force that's acting on something that's not zero something is accelerating and third law is that any two objects that are interacting with each other experience equal and opposite forces as a result of their interaction so if you remember the gravitational force that I was mentioning gravity essentially you are standing on the earth you are um you are being attracted to the Earth that's why you're not able to go flying because you're attracted to the earth the earth is also attracted to you it's just that the force that you exert on the earth is just so tiny as compared to the the Earth's force on you okay the next is motion with constant acceleration and so here um linear motion is these are all very important equations that you need to know and so um let's talk about this one V final = V 0 plus acceleration time change in time so the way that I think of this is let's say I go to the top of the Eiffel Tower and I just um drop a bean bag so my first initial velocity is actually going to be zero because I'm not throwing it downward I'm just holding it and then dropping it so this is zero my acceleration is just going to be the gravitational force so it's going to be you know G and it's going to be pounding it's going to be downward and then based on the amount of time that's passed I can figure out what is the final velocity and so all I really need to know is uh how long does it take to reach the bottom and then I can figure out what was the velocity at the when it hit the hit the ground and so that's kind of how you think about this equation this equation is kind of the same thing uh you just do the squar so V final squ equal V initial squar plus 2 * alpha or sorry 2 * the acceleration times the change in X um change in X is a different way of thinking about it where if instead of telling you how much time it took to get to the bottom I told you how how how tall is the Eiffel Tower and then I and then based on that information you can figure out what is the answer to what was the speed at which the bean bag hit the ground okay change in X which is the change in distance equals V initial time the change in t + 12 Al acceleration time change in t^2 so this is just kind of a different way of um putting this equation you kind of have the same variables but this time you can uh use the the change in time and the change in distance in the same equation and then finally this is the relationship between change in distance and velocity and change in time so this is a pretty um pretty important equation it's pretty fundamental which is that okay let's say that I'm going at 5 miles hour and I tell you that I've uh walked at that speed for 1 hour then that means that I've gone five miles and that's basically what this this is telling me and this is assuming that acceleration is zero and so a different way of thinking about this is that if acceleration is zero then that's just this equation these are the same equations okay projectile motion is something that contains X and Y component so if I throw a football in the air that has projectile motion and if you assume that there's no air resistance which is kind of the resistance that air puts when something is moving through it um then the only uh Force that's acting on something that's you know like the football that's going in the air is the gravitational force that's pulling it down and so the x velocity is going the the velocity of the football is just is just constant and the reason for that is because there's no net force that's acting on that football um that's in the X Direction the only net force that's acting on the football is in the y direction because gravity is pulling it down and so it's important to know that when you're I guess in this example when you're throwing a football in the air there's this this speed at which the football is going in the X direction does not change it's only that in the y direction it's going downward at at some acceleration okay inclined planes there's Force components and so um parallel to the ramp you use S Theta and perpendicular to the ramp you use cosine Theta this is kind of just a a little hack that you can use but you can also think about it and try to figure it out yourself but basically if I'm saying that this thing is going downward we're trying to figure out well um what is the gravitational force how do I calculate that and so since this is kind of sliding down if if I have a gravitational force that's acting on this that goes this way right and I want to figure out okay what is the force that's acting on it in this direction and what is the force that's acting on it in this direction um so how you figure that out is this is the Box this is the gravitation ational force and this Vector is that gravitational force time sin Theta and this Vector is the gravitational force times cosine Theta and so let me repeat that because it keeps disappearing but this Vector is the gravitational force time sin Theta and this Vector is a gravitational force time cosine Theta all right so circular motion um how I always think about this is let's say you have a a rod and then you have a piece of string and it's attached to this little ball and the the ball is going around that Rod right and it's going in circles and you just kind of hold it and it's just spinning like that and so the only Force that's really being acted on that ball is this this tension of the string that's kind of holding it in and so even the ball is even though the ball is going in a circular motion the only Force that's acting on it is the force that's going Inward and so you might ask why doesn't this ball just collapse Inward and that's because it's technically always going inward but it's also just spinning so it is going inward but by the point that I get to this point it's now the gravitational force is this way and so now it's going this way but now the gravitational force is going this way so now it's going this way so it's just kind of always moving in a circular way and so to figure out what the force is that's going inside the circle or what is that tension force it's actually equal to this equation the mass of the ball time the velocity of the ball squar divided by the radius or the distance from that Center Point okay okay let's talk about energy so this is uh not too important the structural proteins but it is important to know how Jewels are derived the unit for jewels and so how I think of it is I think of it using this equation Jews is essentially kilogram time uh met over second and both of those meters over second is squared and so if you take kinetic energy which uh is 1 12 mv^ s this is really important that you know this um if you take the units of this you take the mass which is kilogram and then you take the velocity which is meters over second and you square meters over second you realize that the um that the this kinetic energy is represented in jewels and so Jewels is kind of just a short hand for representing this kind of complicated um complicated assembly of different kilograms and meters and seconds but Jewels is kind of how we represent energy and so energy is um either kinetic or potential uh you learned about this a long time ago potential energy is stored in a system kinetic energy is based on movement so if you have a ball on a hill this ball over here has a lot of potential energy but if it's stationary then it's zero kinetic energy if it's rolling down the hill then its potential energy is decreasing but its kinetic energy is increasing because the velocity is getting faster and faster based on the acceleration then we have gravitational potential energy this is the potential energy based on a on gravity and so again if we have this hill and the ball is at the top of the hill the gravitational potential energy is calculated by mass time gravitational force time height and um this is again in Jewels this thing and then we have uh elastic potential energy electric potential energy chemical potential energy so if you were wondering oh potential energy is this just the fact that it's at the top of this hill there's actually other ways we can get potential energy you can imagine that if you stretch out um this like um let's see if you stretch this you know the slingy thing like that you can if you stretch it out all the way and it has a lot of potential energy because if you take your hands off it's going to like go really quickly and all that potential energy gets converted to kinetic energy so that's elastic potential energy electric potential energy you can imagine something like a battery it's storing a lot of these charges like there's a lot of positive charges on one side and there's a lot of negative charges on the other side and then when you're using the battery these charges flow from one side to the other and that's kind of how very simply that's kind of how batteries work and so it's converting the electrical potential energy into energy that you're using to power whatever device you're using chemical potential energy is kind of when you have um bonds between compounds and then you break those bonds then you're um you know you can convert that potential energy into connect energy so uh you should know the equations for this so elastic potential energy is 12 * K which is this constant based on uh it's called a spring constant it's kind of based on whatever material you're using and then it's x s and X is kind of the stretch or the distance from the center point so if this is kind of how a string is normally um and then you stretch it out like a lot then X is kind of that distance um that you're you're stretching it um and then you don't need to know equations for electrical or chemical potential energy um but it is really important to know conservative versus non-conservative forces so conservative forces are these path independent forces so you can imagine that if I take um a book right and I I put the book on the bottom of a bookshelf but then I put it on the second shelf and then I put it at the top shelf like the 10th shelf but then I put it back into the second shelf the amount of potential energy of this book is actually just the amount of potential energy on the second shelf it doesn't really matter that I put it from first shelf to second shelf to 10th shelf and then brought it back down to the second shelf all that matters is where it is right now but you can compare that to um non-conservative forces and these are path dependent and they cause disspation of mechanical energy from a system so you can imagine that um let's say I have a chalkboard and I'm using um I'm using a chalk right to write a lot of things basically I'm causing dissipation of mechanical energy from that system by constantly writing and causing friction on that um you can also Imagine like um air resistance right if uh I'm um if I take like this uh ball and I move it through the air and let's say there's a lot of air resistance on that day and I keep moving it around and bring it back down um the amount of air the amount of non-conservative forces acting on this is dependent on the path because I basically there's a lot of air friction on this path versus if I just did this there's very little air friction and so the path actually matters and so those are non-conservative forces conserva forces are things like gravity and electrostatic forces if I take two magnets and I put them right next to each other and then I move them really far apart and then I bring them back together it doesn't really matter that I put the like what path they went on as long as they're the same distance apart they're going to have the same amount of force on them so that's a difference that's really important to understand now work work is the process by which energy is transferred from one system to another and it's represented as a DOT product if you remember dot products that's the uh FD cosine Theta and it's also um it's also just a scaler it's not a vector and so you should know that it's f * D * cosine Theta where f is the force D is the displacement power is the rate at which the work is done so it's essentially this divided by the amount of seconds it takes so here is jewels and then if we divide that by seconds then we get kilog time met squ divid seconds cubed because we're dividing by seconds okay the last thing to know is the work Energy System and this is kind of an important concept to understand but it's kind of hard to get into your head and the idea is that when netor work is done on or by a system the kinetic energy will change by that same amount and so if I'm doing work on something then I'm basically adding kinetic energy to that system and if I'm if work if the system is doing work then I'm basically removing kinetic energy and so the change in kinetic energy of that system represents how much work is done is there work being done by the system or work being done on the system um okay mechanical advantage is if you remember from elementary school or middle school there's all these simple machines and so mechanical advantage is the way that a simple machine like a pulley or an incline plane uh kind of helps us to do work and essentially the amount of work that's being done is not changed it's important to understand that but the force the input force of that system is a lot less and so the best example for this is if I was um I was like an Amazon truck uh as an Amazon delivery worker and I had to lift this really really heavy box from here to there right that would take a lot of input force like I'd have to go against gravity but if I if I use this uh incline plane and all I had to do is roll this box up then basically I'm it's the same amount of work that's being done because the distance has increased but the idea is that now my input force is a lot less because all I have to do is just go against just a little bit of gravitational force and just push it along a long distance right and so that's kind of the mechanical advantage Vantage is now my f input is a lot less than it was before where I had to lift this box all the way up this way um so that's what mechanical advantages uh if for an inclin plane it's important to understand that the mechanical advantage is just calculated by how long is this thing divided by how tall it is and you can imagine like a really small inclin plane the mechanical advantage is not going to be that that much like it might be one or something but here the mechanical advantage might be like 10 or something because this is just so long um so the different types of simple machines you don't really need to know this too well but it's incline plane wedge wheel and axle lever pulley and screw and then the efficiency again is the same as mechanical advantage which is the F out divided by the F in and so if you have like a really really um small F in then there's going to be a high mechanical advantage if you have a really small uh High F out then this is going to be pretty big that's the efficiency okay now let's talk about thermodynamics so the zeroth law thermodynamics is that when systems have the same average kinetic energy then they and they have the same temperature there's no heat transfer and so I had a I had trouble understanding this when I was you know studying and essentially if you have like um these two these two parts of component and you have these particles that are moving around um if they have if they're like moving at the same speed and there's the same number of particles um then there's no reason why there would be any heat transfer between these two compartments because they have the same amount of connection itic energy and that's kind of how I think about thermal equilibrium it's not really that important that you memorize these um if you haven't already it would be kind of helpful to understand like oh Kelvin is Celsius plus 273 but otherwise you don't really need to memorize this um thermal expansion these are kind of complicated equations that are just saying a very basic thing which is that when temperature is increasing then this object is going to get longer and it's going to get bigger uh and so this is these are just two equations that describe like the change in temperature is directly proportional to the change in volume or the change in length Okay now is systems systems is kind of important to understand um systems you can have isolated systems closed systems open systems State functions process functions so let's start with the systems you can have isolated closed and open the easiest to understand is open it's when you exchange both energy and matter with their surroundings so there's kind of no um there's no like boundary that's enclosing anything um you can exchange Heat and matter things can go out and energy can go out now a closed system is when matter can't get out like let's say there's a lot of particles in this thing um the particles are not going to leave right um but like they might get slower over time as they're bouncing around because energy is escaping that system finally isolated systems isolated systems are really hard to make in real life because there's no energy that's leaving the surroundings the energy is always staying in there and so these particles are not actually going to get slower when they're bouncing around they're just going to stay at the same speed because the energy is staying contained um they might go slower if their energy is being converted to heat right so they might get slower but now this thing will get hotter and so that um Vel that kinetic energy is just getting converted to heat but that energy is not getting out of that system so that's kind of important to understand um okay uh now we have state functions and process functions so process functions is the pathway from which one equilibrium state gets to another so examples is work and Heat right the the work can get converted to heat but State functions is pathway independent and so it's kind of similar to what we were talking about before but this is basically it's not dependent on the process by which we get there so pressure density temperature volume enthalpy internal energy Gibs free energy entropy these are not dependent on how we got there um so like the best example is probably entropy entropy is like how messy something is so if your room is really messy and not ordered then um then it's high entropy and so it doesn't really matter how you got there whether you organized it 10 times or whether you just let it get messy the entropy is just dependent on that on that um on that final state that you're in it's not pathway dependent um but process functions are kind of how one pathway of equilibrium state gets to another okay um let's go to the first law of thermodynamics so first law of thermodynamics is a statement of conservation of energy um basically basically it's saying that there's a certain amount of energy in the universe it's not going to increase or decrease and so the individual system the change in energy is equal to the energy transferred into that system as heat minus the work done by the system and so this is kind of a cardinal uh equation that you should kind of understand why this is true um because it describes how much this is basically the change in internal energy and it's equal to the energy transferred into the system system as heat minus the work done by the system and essentially in the universe this change is zero um okay so heat is the process by which energy transfers between two objects at different temperatures until they reach thermal equilibrium and thermal equilibrium is again when two things have the same temperature and um this is how I remember this is Q equals MCAT um mass time this constant times the change in temperature represents the heat of uh of that system okay now we have specific heat which is the amount of energy necessary to raise 1 gram of a substance by 1° C or 1 Kelvin and so the specific heat of uh water for example is 1 calorie / G time Kelvin and it's equal to 4.184 jewles divided by GK and so it's um this is kind of something that's going to come up a lot and how you use this is they're going to give you um let's see if I can find an example so this is an example where I found um this on the left the specific heat is low and on the right the specific heat is high and so what you can see is that this is going to heat up easily because it doesn't take a lot of energy to raise this by one degree on the right it takes a lot more energy almost four times the energy to raise this by one degree and so that's kind of how you use specific heat or the Q equals MCAT equation okay next thing is heat of transformation and this is how much energy does it take for phase change so solid to liquid liquid to gas and that's represented by qals ml where L is the heat of transformation now this was always a very tough concept for me to understand which is processes with a constant variable there's isobaric isothermal adiabatic and isovolumetric uh isovolumetric is when the volume is constant and so because the volume is the change in volume is zero the work is zero um and we'll keep in mind this equation when we're looking at all of these processes so work of a gas is equal to P * the change in volume p is pressure V is volume and so isov volumetric is the change in volume is going to be zero and so because of that the work of the gas is zero adiabatic means Q is equal to zero and so there's no heat that's exchanged from the system isothermal is the temperature is constant and so the change in U is zero and the reason for that is because the the when something is uh when the temperature is constant that means there's no change in energy inside and outside the system and so the change in U is zero and then isobaric is the pressure is constant so change in P is zero okay so those are kind of um you can kind of understand them from just the word themselves isobaric pressure isothermal temperature adiabatic heat isov volumetric volume and so this is how you can look at these equations and so um uh if you look at isobaric the pressure is the same right initial pressure stays the same ISO volumetric the volume stays the same right the initial volume stays the same throughout and then we have adiabatic and isothermal so I I was always confused between isothermal and adiabatic especially because the two graphs look pretty similar you can see that isothermal um the pressure is going down and the volume is increasing and adiabatic is kind of the same thing and so the way that I um started learning about it is that let's say that we have this piston right that us see in chemistry class and there's this gas and then the gas is expanding and because the gas is doing work on the Piston so this let's say this is the Piston initially and then the gas is expanding and so because of that the Piston goes up and uh the gas is expanding and so because of that because the gas is doing work it's losing heat right and so when it's losing heat there's heat being exited out of the system um but let's say that we have a heater outside the system and so this gas is staying at the same temperature while it's expanding so that's kind of the difference between adiabatic and isothermal isothermal when we're adding heat the temperature is constant because we're adding heat to the system and it's doing work so it's losing heat but we're also adding heat from the outside um whereas adiabatic is kind of when there's no heat exchange so as this gas is doing work by expanding um and the gas is expanding and so it's losing heat but we're not adding anything so the the the gas is losing heat and it's also Los the temperature is dropping and so that's kind of how I think of the difference between adiabatic and isothermal isothermal is the temperature is constant adiabatic is that the heat is not exchanged so if there's no heat being exchanged Q is equal to zero but the temperature might be changing whereas in isothermal the temperature is constant but we might be adding heat or taking away heat okay um the next thing to understand is the second law of Thermodynamics this is obviously very important and this is all about entropy it introduces the concept of entropy and I already kind of talked about entropy is how much disorganization is there in the system and so I always had trouble understanding this because I I was thinking like um you know this why is this shape more disorganized Than This shape necessarily and it's more about how many different positions can this occupy and so there's only one way you can get these particles to line up like this um maybe you can switch around these particles a little bit but ultimately it's a very organized system whereas there's a lot of different ways that you can allow these particles to spread around and um do that so it's basically the number of states that it could be in so in this one there's only one state that it could be in but this one if you're allowing it to be disorganized then it can be like all over the place it can be like whatever position so there's so many different states and so that's why this is high entropy so whenever you think of entropy you want to think about um how many states could that exist in or how much energy has spread out or how spread out has the energy become and so whenever you think about um your room for example it's really hard to maintain a low end drippy state in your room because you have to keep everything organized but how many different ways can your room be messy so many different ways you know there could be pencils on the ground or books or uh clothes and so that's a lot of different states for it to be high entropy so high entropy in a cloth system um there's for everything up to and including the universe remember we said the universe is we can IM imagine as a closed system because there's no change uh the change in U is zero in the universe the energy is spontaneously and irreversibly going from localized to being spread out and so basically the the ultimate um end outcome of the second law of Thermodynamics is that the Universe kind of dissipates into the highest entropy state which is all heat because we've kind of um we're not able to sustain any low entropy States anymore um okay so that's entropy now let's talk about characteristics of fluids and solids so fluids you know are things that flow and conform to the shape of containers liquids gases um they exert perpendicular forces but not sheer forces it's not too important to know the distinction solids do not flow they maintain their shape regardless of container density is the mass divided the volume and we represent density with this um Greek sign I always forget what the letter is called pressure is the amount of force per unit area so you can imagine that if um I'm putting a lot of force onto a very small amount of area then there's high pressure but if I put the same amount of pressure over a huge area then I'm kind of or if I put the same amount of force against a huge area then I'm kind of spreading out my forces and so it's a weaker Force so pressure is essentially Force divided by area um and remember a gas is kind of like a fluid that goes into its container and so the pressure exerted by a gas on its container is always perpendicular to The Container walls the absolute pressure is when you add the uh so the best way to describe this is kind of with a picture so let's say that I have this right and then I'm kind of trying to figure out what is the the pressure on this right so basically the pressure um is going to be from the air above as well as from this fluid and so let's say that um I have this container and it has fluid and I'm trying to figure figure out what is the pressure at this point right what is contributing to the pressure at this point it's going to be the pressure from all this liquid above that point right all this liquid above this point is contributing to this pressure as well as all the gas up here and so you have to add those two to get this P total and so P total is equal to p 0 plus PGH or sorry the density time gravity time height and so this p 0 is equal to the atmospheric pressure that's being added to this remember like all this pressure over here and then this uh density time gravity time height is basically you have this liquid and you're trying to figure out what is this what is the pressure at this point so you have to figure out how much pressure is this amount of liquid adding to this point and that's what this is for um so this is essentially saying in water every additional 10 m of depth adds one at ATM to the P total and so the um the further down you go you can imagine that there's more pressure being added because there's more liquid above you that's adding pressure okay now we have gauge gge pressure and gge pressure is the difference between absolute pressure and the atmospheric pressure so in liquids the gge pressure is caused by the weight of the liquid above the point of measurement that's kind of what I just mentioned so you can imagine taking this um the P total and then subtracting it by the P atmosphere and that's kind of how you get the gge pressure so if I were just to tell you what is the the pressure at that point and then you knew the atmospheric pressure you can kind of figure out what is the pressure that the liquid is adding next is hydrostatics so there's Pascal's princip principle which is that a pressure applied to incompressible fluid will be distributed undiminished throughout the entire volume of fluid and essentially it means that let's see if I can find an example so the best way to describe Pascal's principle is with this picture and basically where there's the same amount of pressure at P1 and P2 um and so um basically we apply this force over here and we're applying this force over a very small amount of area and if you remember what I was talking about pressure it's force over area right and so that if the denominator here area is small and the force is you know I'm just pushing my hand down so the the pressure is going to be pretty big because the area is so small and then here the area is really big right and so this area is going to be bigger and this pressure P2 has to equal P1 according to Pascal's principle because the pressure is equal throughout and so because of that this output force is going to be pretty high because my my input pressure is going to be the same as the output pressure here right if the input pressure is high P2 is high A2 is is high right so A2 * P2 you can imagine that F2 is really high and so that's why we're able to just by pushing down with our hand for example we'd be able to lift up this car and so that's kind of another example of mechanical advantage so that's Pascal's principle that's always how I remember that then we have hydraulic machines and that's that's exactly what I was talking about that that was an example of a hydraulic machine and then there's Archimedes principles Archimedes principle is that when an object is placed in fluid there's this buoyant force against the object that is equal to the weight of the fluid displaced by the object so this is kind of hard to understand um until I was watching uh this Con Academy video about it and it explained it really well which is that when you have this all this water and then you put a ball inside there's going to be a buoyant force that's pushing this ball upward and the best way to think about that buoyant force is that this ball is competing with water to be in in here right there's all this water and now this ball has pushed up some of the water and so all that water wants to come back into into that space that the ball has occupied and so the the force that the water is uh putting onto this ball to go back up is is dependent on how much uh water has been displaced by this ball and so you can see that the force the buoyant force is equal to that density density of the fluid times the volume and if you can calculate this this is actually just the mass right times the gravitational force and so basically then that's what this is saying over here so basically the buyant force is equal to the mass of the fluid times the gravitational force and that's what is pushing this object back upward now the density this is another important equation which is just based on what I just told you which is that the density of the object divided by the density of the displaced fluid is equal to the weight of the object in air divided by the weight of the object in air minus the weight of the object in water and so this is um essentially saying you don't need to memorize this equation but you need to understand why it works essentially what this this equation is saying it's best to describe this by just giving you two examples so let's say that the density of our object the ball that I was talking about let's say the the ball is a bowling ball and so it's a really high density like it's very heavy for how much space it takes up if that density is very high then what that is telling us over here this this number would be really high and so what that is telling us here is that the weight of the object in air is going to be really high right so it's going to be a heavy object um and that this difference is going to be pretty minimal so the weight of the object in air is going to be kind of similar to the weight of the object in water because this has to be pretty close to uh one or zero for it to be true but if the density of the object let's say the object is like a beach ball right it's very low density that means that this is going to be pretty high right so the denominator of this is going to be high if this is a low number and so so if the weight of the object in air minus the weight of the object in water is a very high number that means that the weight of the object in air is very high compared to the weight of the object in water and so you can kind of Reason out uh what this is saying which is that the weight of the object in water is going to be pretty low and that's kind of true of a beach ball it's not going to be very it's the weight is not going to be very heavy it's not going to be very large in water versus a a bowling ball the weight of the object in water is going to be pretty big and probably pretty similar to the weight of the object in the air that's what basically this equation is saying you don't need to memorize it but just if you can understand that reasoning that'll be helpful if the max buyant force is larger than the force of gravity then the object's going to float so that makes sense so if this force is greater than this Force then it's going to float but if the buoyant force is lower than the force of gravity then it's going to sink so that's just kind of self-explanatory and then that's that's what this is saying too okay next is specific gravity specific gravity is the ratio of density of an object to the density of water and so if I told you that you know a bowling ball has a density of four and water has a density of one then specific gravity of that object is four cohesive versus adhesive Co fluids have cohesive forces with other molecules of the same fluid so cohesion is like why water forms droplets because they're all um C cohering to each other and then adhesion is that it sticks to other material so that's why water sticks on a window shield for example because it's adhering to the window shield surface tension um because of cohesion these water molecules are sticking together and that's why um like um crickets are able to walk on water I forgot which insects are able to um that's why because there're surface tension okay hydraulic lifts this was the example that I was giving you with the um hydraulic machines and pascals principle which is that if you have a force that's being applied here and then this force is being applied here the pressure is throughout this liquid because it's continuous has to be the same and so this output force F2 is going to be really high even if this F1 is not that high because the area is just so much larger here okay the next is fluid dynamics we have viscosity laminar floor and tub tubular floor so viscosity is how much internal friction the fluid has a viscous drag is a non-conservative force generated by viscosity and actually in med school one of the things we um we learn about is all these different uh diseases and autosomal um dominant diseases that are caused because blood just gets so viscous and there's that causes like strokes and things like that because there's not enough blood getting to the brain and things like that so that's kind of the medical connection to this laminar flow and tubular flow laminar flow is smooth tubular flow is turbulent flow is kind of like an airplane when it's really Rocky it's very rough and disorderly P's law I've never known how to say this but it basically determines the rate of lamin flow so it's assuming that this it's smooth and orderly if there's a lot of bumps and edges then you can't use this law but basically it says that Q which is the flow is equal to Pi * the radius so radius is you're assuming that this is going through like a blood vessel or or some uh Rod right the radius is the the distance from the center to the to the edge times the change in pressure equals 8 * this density * l so the equation is Q which is flow * pi * sorry Q equals Q which is flow equals Pi * radius to 4th * change in pressure uh / 8 time a constant this constant is dependent on the viscosity of the fluid so it's dependent on the fluid at hand times the length at which you're looking at and so that's what this law is equal to and the relationship between radius and pressure gradient is inversely exponential to the fourth power and that means is that if somebody asks you like um if the blood vessel gets larger does the does the pressure gradient get smaller or larger and the answer is that the pressure gradient gets smaller because they're inversely proportional so radius really affects how much pressure gradient there is um and this P initial is going to be larger than the P final so there's there's less pressure at the final pressure than the initial pressure and that makes sense because you need a lot of pressure to to get it from here to here and so um that's why this fluids flow from high pressure to low pressure okay now we have flow rate flow rate is flow Q Divi is equal to volume divided by time so basically if we're looking at a blood vessel how much blood is getting across this in a certain amount of time a is the cross-sectional area and V is the velocity so another way to measure this is what is the cross-sectional area of that blood vessel times what is the velocity of blood that's going through that cross-section okay now we have the continuity equation and continuity is basically saying that we're going to have the same flow rate throughout the entire um blood vessel for example or the entire pipe so if this is um a a pipe and then it's getting larger over here the flow is going to be the same over here as it is going to be over here and so you might ask like how is that possible and the reason that's possible is because the velocity is really high over here and the velocity is really slow over here because it gets so wide and so V1 over here is really high even though A1 is very small and then V2 over here is very small because A2 is really large and so there's basically uh Continuous Flow throughout entire blood vessel or entire like any any form of Lamina flow will have continuous blood flow okay beri equation is basically that the sum of static pressures and dynamic pressures is going to be constant between any two points in a closed system and so basically this is going to equal this um and I think it'll make more sense as we go on but I will come back to this and explain this as we get through more terminology okay so this is basically the best image I found for br equation and um you can see let's say that I took a point right here and I took another point right here okay the first thing I want you to notice is that this and this are going to cancel each other out because the potential energy at this point is equal to the potential energy at this point because the height of height one and height two are equal so that makes it really easy because um because these two heights are equal we can cancel these two out and so now we're looking at P1 and then the velocity one as compared to P2 and the velocity 2 to figure out the energy so remember um because this is a single system with laminer flow we're allowed to use this equation and so there's some Force that's being applied here that causes P1 to have um to have to be greater than P2 and that's why the whatever the liquid is Flowing this way right because there's it's going down its pressure gradient and so because of this Force P1 is going to be higher than P2 but let's first focus on V1 and V2 where do you think um the fluid or blood is going to be moving faster at this point or this point it's probably going to be moving faster at this point because if you remember Q equals AV right and um we know that Q is going to be the same throughout this entire thing and so because this a is much smaller that means V2 is going to be much bigger and so this V2 is is Big right and this V1 is small so that's kind of how you can think of that and we know this P1 is going to be bigger than this P2 and the reason for that is because there's forces that are acting this way and pushing this Blood this way whereas there's less Force that's being applied this way to this object and moving it this way so to reiterate what I said A2 is smaller than A1 this A1 obviously is bigger V2 is greater than V1 and that's because this A2 is small so V velocity is really high here and the final thing is that the pressure at this point is higher than the pressure at this point okay and that's why fluid is Flowing this way because it's going down its uh pressure gradient uh and remember br's equation is basically saying this is equal to this okay the next thing to talk about is the Venturi effect the Venturi effect is that velocity of a fluid uh going through a constricted area will increase and static pressure will decrease and that's kind of what we just mentioned which is that as we're going from this really um really wide thing to this really narrow thing basically the velocity is going to increase because this area is decreasing and then the static pressure is decreasing and that's because it's going into this and we know fluids goes down this pressure gradient so it's going from high pressure to low pressure low speed to high speed okay the next thing to know is the Venturi tube and I'm going to show an image of this to make it uh more uh more understandable but basically we know A1 over here and we know A2 over here so what do we know based on that we know that the velocity is going to be really high over here as compared to over here okay then we know that we're looking at this point and we're looking at this point so we know that the heights are equal and because of that the P the density time gravity time height is going to be equal at both points so because of that because we know velocity is higher here we know that the pressure must be higher here and so that's why because the pressure is higher over here that's why this is elevated because there's more pressure versus at this point there this is less elevated because there's less pressure it's it's moving more this way and so that's why this fluid is sticking up and you can figure out the pressure difference by just calculating this height and multiplying it by the gravitational force times the density of the fluid okay now we have fluids and Physiology and this is the circulatory system the circulatory system behaves as a closed system with non-constant flow um so uh the non-constant flow is our pulse and so this is kind of what I've been alluding to by talking about our blood vessels um V is velocity Q is the flow and then area a is the cross-sectional area this is the equation we just looked at and then now is where we kind of compare this equation with this equation so we know that the change in pressure is equal to the flow of the fluid or the blood in our body time R which is the resistance and in our body the way that we get resistance is based on these uh arteries and arterials that are kind of constricting and expanding and that's how we get resistance so here this is basically saying that our pressure change is equal to the flow times the resistance resistance and so um another way of putting that is by taking this equation the VA and then putting that in the Q and so we get VA time resistance and so pressure is directly related to Velocity area and resistance area is inversely related to resistance and velocity and then as our cross-sectional area increases so this guy the a then that means our resistance is decreasing and or the velocity is decreasing so as this goes up this and this must go this or this must go down the V or the r okay next we're talking about breathing and again these are all clinical correlates of um physics so these are kind of the ways that they'll test you when you're reading the article so breathing basically inspiration and expiration creates pressure gradients um not only for the respiratory system but for the circulatory system too and so you can imagine that when you're breathing in your diaphragm is going down and so in the respiratory system basically your lungs are getting larger and that creates a pressure gradient where your lungs your um because your diaphragm has gone down your lungs have expanded and there's less pressure in your lungs and so the higher atmospheric pressure goes into your lungs because now your lungs have expanded there's less pressure and so you're breathing in and then when you're breathing out your diaphragm goes up you have more pressure in your lungs than outside and now your air is going out and so that's how breathing Works um alvioli are the these little things in your lungs that allow for gas exchange and air at the Alvi essentially has zero speed okay next is electrostatics and magnetism electrostatics and magnetism is a very high yield Concept in physics um um so let's talk about charge kums is the SI unit of charge we have protons and electrons and um we made it really simple because we have this thing called uh that we just say as e and that kind of represents the charge that a proton or electron has and and it's equal to 1.6 * 1019 Kum and so both protons and electrons fortunately for us has the exact same fundamental unit of charge attraction and repulsion is um you know when you have a proton an electron they attract when you have an electron and electron they repel things that have opposite charges attract conductors and insulators are also important in circuits conductors allow electrons to move and then insulators don't allow uh things to move in a circuit they resist the movement of charge um and we'll have localized areas of charge that do not distribute over the surface of the material okay now we have kum's law kum's law is that uh you have the magnitude of electrostatic force between two charges and so if I have a proton and a proton then these two things are going to go apart from each other right and what is that Force called that force is given to us by kum's law which is this so it's this constant times q1 the charge of the first um particle times the charge of the second particle divided by the distance between them squared the electric field um another thing that I always got confused about was this R like does this R mean half the distance or the full distance it means the full distance so this particle and this particle the r is the full distance between them electric field is um basically if I have a proton over here right it's going to generate an electric field around it and the electric field is basically telling me what happens if I put another particle over here and so electric field is answering that question by telling us oh this this proton over here is going to cause this force on this particle if you put it over here and so the electric field is basically this imaginary field um around a particle that tells us this imaginary field around a particle that tells us if we add a a positive char a proton around this particle what's going to happen to it so if I put a proton over here oh this force is going to push it away if I put a proton over here oh this force is going to push it away if I put a proton over here oh this force is going to bring it this way so basically electric field tells us if I add a proton to this field where is it going to go so in this system I have like an an electron and a proton so if I put a proton over here where is it going to go it's going to go this way if I put a proton over here where is it going to go it's going to go that way so that's what an electric field is a very simple explanation of electric field um so how you calculate what the electric field is is you just do the force divided by the charge and so then you get k q / R 2 and I always used to get confused by what is this Q value over here and basically it's just telling us that oh if I have a proton over here what's the electric field well the electric field is just going to be this um this particle you take that charge okay to find the electric field all you have to do is to take the force that's exerted on that test chart so if this is the the charge that's creating the the electric field right and we have all these lines that are the electric field and then we have that other um charge over here we kind of just ignore this charge that this the electric field is just dependent on the charge that's creating that electric field and so all we have to do is just take what we would calculate as the force between those two charges and then divide that by the charge that we're kind of ignoring here and so electric field is just K * q and this Q remember is just the the the charge that is creating the electric field divided by the distance between the two charges squared so that's how you how you calculate the electric field now the next thing to know is field lines and we just talked about this and field lines show the activity of a positive test charge so if I put a positive charge that's the direction the field line tells us the direction that that positive charge would go in okay equip potential lines are just if we draw a parallel line to our um to our electric field lines that's how we get equal potential lines and this is an equipotential line okay this is our equip potential lines so remember this is the electric field line over here that is pointing out from the positive charge in the middle but then these are electric equip potential lines which are perpendicular to those electric field lines so these circular things around and basically what that's telling us is that at all these different points along these equip potential lines there's the same amount of potential that a charge has and so to move a particle from here to here it requires no extra work um but to move a particle from here to here on different equip potential lines that takes a lot of work because you're let's say this is a positive charge to move that positive charge so much closer to this other positive charge that's going to take a lot of work and in the same way if we take a a particle and we move it away right to a different equip potential line then there's there's going to be work done by the system because it um the the positive charge likes to be out here away from the other part positive charge so that's kind of what equipotential lines are okay the next thing to talk about is electric dipoles and electric dipoles are just um when you have a positive charge and a negative charge right next to each other and basically all this is saying is that there's going to be a net torque on this dipole when there's an when it's situated in an electric field so let's see if if I can find an example so here's an example of what that is talking about which is that this is a dipole right there's a positive particle here and there's a negative particle here and this is situated within an electric field and the electric field lines are all pointing this way and so what's going to happen is that when there's a dipole in an electric field the dipole actually doesn't um move translationally like it doesn't move this way or this way what actually happens is that there's just torque on it and so the electric field is just going to move this way um because this is the positive charge and this is a negative charge and so that equation that we were looking at before over here tells us well sorry this equation over here tells us what is that torque going to be and that torque is equal to this this p over here is just the vector that is created by the the dipole so it points from one of the charges to the other charge and this is the electric field that it's situated in and so it's just the cross product of that and that describes the torque that we have and remember this torque is a vector the other thing is this equation which is the voltage and this is just describing well what is that so here I've just pulled up an interpretation of that equation and essentially it's just the electric static potential due to a dipole and so V just like normal is the potential the electric potential and K is the kum's constant Q is the magnitude of the charge D is the distance between the charges and R is just the distance from the dipole to the point at which the potential is measured and so by that you could get the voltage of a dipole now the dipole moment is just very simple it's just the distance between the two charges times the charge itself okay now these are the important equations that you need to know um for electrostatics and mag just electrostatics actually and uh we've already talked about Force we've already talked about electric um electric potential sorry electric field this is electric field this is force now this is electric potential kqq over R so just remember that the difference between this is that there's no R squ and then we have voltage and voltage is what we're going to talk about next so just know these four equations they're all interrelated and all very similar the next thing is electric potential energy so electric potential energy is the amount of work required to bring the test charge from infinitely far away to the given position so to give you an example let's say I have this charge over here um this positive charge and then I have this positive charge all the way out here at Infinity right the electric potential describes how much work is it going to take to bring that charge right next to this positive charge right and so that's what electric potential energy is because these forces don't like to be next to each other this is going to to repel so the fact that they exist close by to each other means that there's some potential energy and if we release these two charges then they're going to go flying away from each other and that's that's why there's electric potential energy when two positive charges or two negative charges are right next to each other um this is the equation again kqq over R is the equation for electric potential energy and next we have electric potential energy so electric potential energy is what I just described and electric potential energy is related to Vol voltage because if you just take the electric potential energy and divide it by that charge then you get voltage now voltage is just the potential difference um from one spot to another spot and this is how batteries work is that there's going to be a voltage there's going to be a potential difference in these two places and because of that potential difference there's movement of charges from one place to another and because there's movement of charges within a battery or um because a battery has potential when you add that battery to a circuit and everything lights up because now suddenly the battery is allowing charges to move from high potential to low potential So within your battery you have a area of high potential and you have an area of low potential right and these two are just separated by a little bridge and then you have a circuit and now all these charges go from high potential to low potential or from low potential to high potential depending on whether we're talking about negative test charges or positive test charges positive test charges go from high potential to low potential and negative test charges go from from low potential to high potential not that important that you know this but very important that you understand voltage voltage is the difference in voltage can tell you about the work that is being done so the work from point A to point B divided by the charge is equal to the voltage difference and that's basically how batteries work in circuits okay the next thing to talk about is magnetism and um with people who have tutored magnetism is the thing that really trips a lot of people up and and um the reason for that is because a lot of people think that uh electric fields and electric forces point in the same direction as magnetic fields and magnetic forces but that's not true and I'm going to talk about umic field okay this is a magnetic field right this is a electric wire and essentially any any moving charge so let's say this is a proton and it's moving so if a proton is moving this way then it creates an electric field around sorry it creates a magnetic field around it so we know that protons already create electric Fields right and this electric field is going like this well if it's stationary there's no magnetic field but let's say this proton is actually moving if it's moving then it creates a magnetic field as well negative charges also create magnetic fields if they're moving so now let's talk about this wire now this wire let's say that it's moving this way and these are the electrons that are moving up now we can use the right hand rule and figure out well which direction is the magnetic field in and essentially we point our Thumb in the direction that the negative charges are moving in and then you wrap your right hand and it's going to look different because my camera is inverted but you you do this by yourself take your right hand and then just curl your right hand around and you'll figure out what is the direction in which these magnetic field lines are moving and that's that's how you figure out the magnetic field so if you look at this example over here this is the same thing which is that we see which direction is our current moving in and then we figure out okay based on the right hand rule I can figure out which way is these magnetic field lines going okay so it's all dependent on current just remember which way electric current is going so one really quick correction I want to make on something I just said is I describ this current moving and how that creates the magnetic field so this current represents positive charges that are moving this way and those positive charges then you use the right hand rule and then you figure out what is the direction of these mag magnetic fields that is created by that wire by these positive charges moving but if we had if we were told that electrons were moving in this direction then this magnetic field would point in the opposite direction so the current represents the positive charges that are moving that always confuse me prior and I just want you to make I just want to make sure that you guys understand that so that was a quick correction okay the next thing to talk about is um these two equations they're not going to show up too much but I would just try to remember them which is that these this is the magnetic field that is created by a straight wire and this is the magnetic field that is created by Loop of wire and I can show you a loop of wire magnetic field which is that it would look like this where um yeah this is a good example where you have this this loop loop of wire and there's a current that's going through it and because of that there's going to be a magnetic field that's created by that Loop of wire um again not not too high yield but that uh might come up okay the next thing is diamagnetic materials paramagnetic materials and ferromagnetic materials now ferromagnetic materials iron iron has a lot of uh is very magnetic right so you can kind of know based on that that um it's going to be strongly magnetic there's some unpaired electrons diamagnetic has no unpaired electrons and are repelled by a magnet and then paramagnetic are in the middle they have some unpaired electron and they're weakly magnetic now we have characteristics of magnetic fields now characteristics of magnetic fields it's important to know that any moving charge can create a magnetic field so in addition to that external magnetic fields also in uh exert forces on charges that are moving in any direction so let's say I have um I told you that okay I have this really strong magnet and it's causing this um magnetic field and this magnetic field is represented by these x's and um I remember being confused in physics class by these x's and dots and X's basically mean that the magnetic field is going into the page and dots mean that magnetic field is going outside of the page so again let's say that the magnetic field is all xes if there's a electric charge like a proton that's moving through this through this magnetic field then there's going to be a force that's acting on that uh moving charge okay so let's say the moving charge is moving downwards and it's within a magnetic field now this there's going to be a new Force that's acting on sorry this should be X's now there's going to be a new Force that's acting on this moving charge and so now this moving charge might move in a slightly different direction because it's within this magnetic field so I think it'll be easier if I show you an example this is a good example of what I'm talking about so let's say that there's this magnetic field and again x's mean that the magnetic field is going into the page so this mag there's a remember that this is the magnetic field and this magnetic field is created already it's not from these moving charges these moving charges are now moving within this magnetic field and let's say that this positive charge is moving this way so up and to the left within this magnetic field now there's this there's this equation and the equation is represented by QV cross B and that represents the magnetic force that's acting on this particle within this field and it's dependent on the direction that this particle is moving so let's do the cross product of the Velocity which is in this Direction with the magnetic field which is again going into the page and I want you to do the right hand rule and remember it's kind of the opposite with my hand because I'm my camera is inverted but you take your right hand and you point it in the direction of the velocity so it should be going up into the left and then you curl your hand into the page and what you should get is that the positive charge points in this direction okay now remember when I mentioned that these are always for positive charges so when you're talking about negative charges like when I was talking about the current in the wire you represent that as positive charges that are moving through it and if you have a negative charge that's moving through it then you just reverse the direction so the same thing goes with this Force so now we have a negative particle and it's moving in this direction so again use your right hand rule Point your hand in the direction of the velocity and then point your hand into the page and then you point your hand and your point hand should be pointing up and so if this was a positive charge it would be the force would be pushing it upward but instead the force is pushing it downward because it's a negative charge and so that's just kind of a helpful way to understand which direction is the force pushing this moving particle in okay so again that's the moving point charge and then the same thing goes for a current carrying wire if you have a wire and it's within a magnetic field there's also going to be a force on that and let me see if I can find an example for you now let's take this as an example so we have two wires and they're parallel and both of them have electric currents that are pointing in the same direction so you should be thinking okay based on the right hand rule I know that this is going to move in this direction this magnetic field and this is also going to move in the same direction right okay so based on that we should know that when this this let's say this first wire is exerting a magnetic field on this second wire so this second wire the the current is moving upward right so that's our V our velocity or I should say our I right and remember our equation if I go back is um I L cross B so we want to take i l and then cross it with b and so we take I which is um this this this is our I vector and then L and then cross it with b and our B Vector is again this one right here if you map out where this is when you get to this point it's moving in this direction so if we do the right hand rule then we'd get what this guy is showing over here which is we point our hand upward we curl it in and we see that this is pointing to this way and if you do this same process with this wire the you'll see that this points this way and so basically when you have two wires that both have current moving in the same direction and both wires are parallel those wires are going to come together because there's a force that each other is attracting to its so so that's kind of how you can think of wires and uh if you can remember that then it'll be pretty easy to remember these two equations so just remember these two equations and you'll be solid um and remember these are just cross products between QV and B and this is a cross product between I and B okay the next is Lawrence Force you don't really need to know this but it's the sum of the magnetic and electric forces acting on a body it's like a free body diagram but instead of um translational forces it's electrical and magnetic forces okay the next thing to talk about is charges and then we get into the fun stuff which is all these circuits so charges we have current current is again the movement of charge that occurs between two points point of different electric potentials remember current is what happens in a circuit and current again this is where I always used to get tripped up and that's why I made that additional segment where I was talking about my mistake which is that current is defined by the movement of positive charges from high potential to low potential in reality it's electrons that move in the circuit but the way that for some reason somebody decided that we will think of current as POS movement of positive charges so it's just um it's just kind of a semantic thing of how we decide to uh Define what current is so current is defined by the movement of positive charges but really what's happening in a circuit is electrons are moving not protons okay and then how do we Define Uh current it's basically how many charges are moving through some point uh over some amount of time so in one minute if we have like a thousand electrons that are moving through a point then that's how we just find what the current is so current is I okay conductive materials so you should know that there's um conductors and there's insulators so metallic conductors allow the flow of current electrolytic conduction means the movement of free ions under electric field and then finally we have insulators insulators are materials that don't have a current so it's really important to know metallic conduction and insulators electrolytic conduction is not that high yield okay kersh's laws are basically these are very high yield um it's probably going to show up at least once in your exam which is that um the current that's going into a junction is equal to the current that's leaving a junction and we'll go into an example I'll show you on Google Images an example and then we have the loop rule which is that the sum of all the voltage sources equals the sum of the voltage drops so this is V Source equals V drop and so let me show you an example on Google Images so this is a good example of what I'm talking about in kers Chef's law so the current law is essentially that um the current that you're entering a junction with is the same as the current that you're leaving the junction with so this I total over here is equal to the I total over here because this is what's coming back after you're done with all the Junctions and this is what you're going into the junction with now the current gets split up over here and over here when you get to the parallel circuits and then when it comes out of these parallel Junctions and comes back it sums up and it comes back to I total so i1 plus I2 equals I total which is the same as what you started within the circuit now how do you how do you know how much of current goes in this part and how much of the current goes in this part well it's just dependent on the resistances of those two parts of the circuit and so that's kind of you you take the the voltage and then you divide it by the resistance and you figure out the current over here now in this example it's just a it's just a series it's not parallel and so the the current stays the same throughout the circuit now what about voltage what happens to voltage this is kind of a good example of what Kira's law is saying which is that the drop in voltage across this uh and then across this and then across this and then across this the after you take after you add up all the voltages you get the total amount of voltage right and then the drop in voltage is equal to zero so if I start out with nine volts and then I use two over here and then three over here and then three over here and then one over here then that that's what kop say you're not going to Res you're not going to have any left over voltage in the circuit all the voltage will be used if you only have one resistor in the whole circuit then all of that nine voltage is going to be used in that one resistor so that's what cir Shop's law is okay again make sure you know that that's pretty high yield now resistance is the opposition that a substance offers to flow of e resistors are um you can think of them as conductive materials with a lot of resistance um that slows down electrons without stopping them because if you stop the circuit then there would be no flow but there is some flow it's just that it's creating resistance in our circuit um and this is kind of how you figure out resistance it's um you're not going to have to calculate resistance but it is helpful they might tell you like oh if we increase the length then what's going to happen if we increase the cross-sectional area so just know cross-sectional area is on the bottom length is at the top resistivity is at the top and that's what describes resistance okay ohms law is super super high yield make sure you know that V equals I and that's kind of how you figure out how much voltage drop is on is happening across each resistor okay if you add up all the resistance in series then you get the total amount of resistance and then if you take the reciprocal of the resistance and parallel and you add them up then you get one over the total res the total resistance so um I was always confused about this until one day somebody much smarter than me in our physics class asked well why does resistance drop when you go in like in parallel why is the total amount of resistance in this circuit less than if there was just one resistor and the reason for that is my physics teacher explained like imagine that this there was traffic and it was going through a traffic jam but instead of just one row like there was in series now you have three options for the cars to go well obviously the cars are going to go a lot faster because now cars are going across three different places and so that's why the total resistance in a parallel circuit is less than the resistance if you just like let's say that the this resistance was 200 this resistance was 300 this resistance was 500 um the if you just had this total resistance might be like 50 it might it's going to be much less than these three resistances and the reason for that is because the the traffic of the electrons can now go in any one of these and so there's going to be a total less amount of resistance so that's how you can think of parallel circuits okay now you have capacitors and capacitance okay capacitors have the ability to store and discharge electrical potential energy so let me show you an example um so capacitors are kind of they look like this but in a in a circuit what you'll look like what they'll look like is like this thing like two lines and essentially it flows through this capacitor freely but it'll store charge so it'll kind of act like a battery where there's a voltage uh difference on on that capacitor and what you'll notice is that there's a series of equations to determine what the capacitance value is and so capacitance store that um that voltage that's coming from a battery and then they discharge that electric potential energy when they need to and so a capacitance this is the really important equation over here which is Cal Q / v v is the voltage difference across the plates and Q is that charge that's being built up so if there's a plus 9 on one side and then a - 9 on the other side Q is 9 where 9 represents kind of like the the electrons and protons that are building up on one side okay um it's also it's really important to know that the greater the area the greater the capacitance the greater the distances between these two plates the smaller the capacitance that's what this equation is telling us this constant over here the E KN that's based on the material of the capacitor okay electric field in a capacitor is equal to eal V / this is also a really important equation to know so they might ask you oh what's the electric field that's created by the capacitor and it'll be equal to the voltage that's created by the capacitor divided by the distance between the two plates okay now we have potential energy of a capacitor this is also important and that's equal to U equals 12 cv^ s so that's important C is the capacitance V is the voltage okay now it's important to know and we'll go into this that these act the opposite as resistors in series and parallel so so parallel is they create a larger capacitance and series they create a smaller capacitance finally there's that um K constant the dialectric constant and this just tells us that um insulators when they're placed in between the capacitor so let's say I have an insulator right in between this that's going to increase the capacitance by a factor called the K Factor the dialectric factor um and so the way that you can think of that is um before there might be an El that can fly from here to here in the capacitor right and um that means that this capacitance is is not as strong because uh it's trying to create voltage difference across these two plates but some of the electrons are flying but then imagine that you put a resistor in between those two plates right now there's not going to be as many electrons that are flying and so now you can have a stronger voltage difference and that's kind of how you can think about why insulators between capacitor plates can increase that capacitance okay now there's me these are the things that you used in physics lab to kind of measure you know the volt to measure the resistance and to measure the current and that's what those do so um an meters have negligible resistance they measure the the current and you have to put them in series and why do you put them in series remember the ohms law that I was talking about now there's voltmeters voltmeters you have to put in parallel and that helps you measure a voltage drop because they have very large resistance so remember when you're going into a junction this is kind of what's going on with the voltmeter you basically put the voltmeter right here and then you can figure out what is the voltage drop across this um that's again because of ohms law so make sure you understand this according to ohms law if you understand ohms law you should understand why this is in parallel and this is in series and finally you have oh meter which is to uh insert it around resistive element and that measures resistance so just know those those are kind of just vocabulary terms but make sure you actually understand this um connection to OHS law okay next is capacitors in series and in parallel so capacitors in series remember I told you that when you have in series it does the opposite of resistance so this is kind of looking like this in parallel where you take the reciprocal you add them and you get the reciprocal of that and that gives you the total capacitance and here it's just the opposite you add up the capacitance when you're in parallel and that gives you the total capacitance so I just kind of remember it that it's the flip-flop of resistance if you remember that you'll be fine okay the next topic is waves and sound and I really like this topic so transverse waves is kind of like light it's when you have um oscillations of a wave particle perpendicular to the direction so this is actually what transverse waves look like and um I this is not to over complicate it but light has remember those dual properties of particles and waves so this is specifically referring to that wave like property and mostly when you think about waves it's going to be kind of like this where it's like sine waves or cosine waves these are transverse waves that where they have oscillations and they're perpendicular to the direction of the movement direction of movement is this way okay next you have longitudinal waves and longitudinal waves is like sound so this is a longitudinal wave and this is a transverse wave so this is kind of like how sound moves which is that there's just a lot of these particles and they're bouncing off each other and that way they move this way because the the uh vibrations will eventually go from where the sound originat to your ear and that's what longitudinal waves look like this is what transverse wav looks like okay um next we have all these equations this is very important for you to know um you should know that uh wave speed is equal to frequency time wavelength and then um you should know that frequency is kind of how many of these waves happens per second or per unit of time and then the wavelength is um how long are these waves right and you measure it from like Crest to Crest or trough to trough or any point to the next Point um so that's how you measure wavelength okay the next thing is this equation over here and basically you don't need to know they're not going to ask you like specific values of this equation to plug in but it's kind of important to understand what the meaning behind this is so B is bulk modulus and what that means is and this is basically saying wave speed so the best way that I always remember this is that um in the first grade my my teacher asked us to put our head to the desk and then we had to knock the uh desk and I remember it being really loud when I put my ear next to the desk versus when I just knocked the desk and my ear was in the air it was a lot less loud and so the way that I remember that is that the bulk modulus this gets bigger when we go towards a solid and smaller when we go towards a gas um so that's that's this thing but then within that material so when we're in a solid the less dense that solid is the greater the wave speed is going to be so that's kind of counterintuitive because solids are greater density than gases but you want to know that if I'm talking about a solid then this numerator is going to be high but if I'm talking about a very um if I'm talking about a solid that's not at all dense then this denominator is going to be low and so this wave speed is going to be high so the gases have the least amount of wave speed solids have the most amount of wave speed once you get to a solid the least dense solid will have the greatest wave speed so that's how you think of that equation displacement is how far a point is from the equilibrium position so if I was talking about if I was like right here this would be the displacement the displacement is greatest at the crest and trough and that's what the amplitude is referring to um and then you have amplitude which is the maximal displacement what I just talked about then we have wavelength which I just talked about frequency which is the number of cycles per second and then you have angular frequency um this is kind of just the angular displacement per unit of time and that's just a different way of representing it which is 2 pi ided am amount of seconds or 2 pi times the frequency okay then you have period period is just how number of seconds that it takes to complete a cycle so it's the inverse of frequency and then we have interference interference is kind of how these waves interact with each other so you can have constructive interference where you have two waves and they kind of look similar and so they just add up with each other or you can have destructive interference where you have two waves and they're kind of out of sync and so when you add them up then they're just kind of sum up to something less than the total less than the sum of the parts so destructive interference might end up in like these smaller waves or it might just end up in a straight line and so that's kind of the destructive interference versus constructive interference now you have partially constructive and partially destructive interference so destructive interference the way that there's describing it is that it results in like just a straight line partially is that when you have like it's kind of out of sync but it still ends up in like some wave form right and so you might still have like it might not be a straight line if you add these up but you'll have like a little bit okay traveling waves versus standing waves so traveling waves you have continuous ly shifting points of Maximum and minimum displacement and standing waves is just when you have constructive and destructive interference of two waves with the exact same frequency traveling in opposite directions so standing waves you're going to have um like perfect destructive interference versus traveling waves you'll have shifting points of Maximum and minimum displacement let me see if I can find you an example so this is a good example that kind of explains what I was saying a standing wave is kind of like this where it doesn't move it's just kind of stationary and then traveling waves you can see a video of this um but traveling waves it's kind of going up and down and up and down and up and down so then it might look like this after that and then it might look like this for a second and then it'll look like this it's basically traveling so that's what that's what that difference is okay um so again traveling waves have continuously shifting points of Maximum minimum displacement and standing waves is just the same frequency traveling in opposite directions in the same space anti noes and nodes so nodes is where there's no oscillation anti noes is where there's maximum oscillation so if we looking at this wave over here this is the node and this is the anti node because if we think about this as a traveling wave then this is one point and then this is another point and then this is another point so you can see no matter how it's going like if we take two parts of a string and we like move it up and down no matter what this place is always changing as amplitude and these things are not changing so that's what node and anti-node means then we have resonance resonance is the increase in amplitude that occurs when a periodic force is applied at a natural resonant frequency and we're going to go more into resonance in a little bit um but yeah just understand like resonance is kind of related to what we'll look at over here um okay damping is the decrease in amplitude that's uh caused by applied or non-conservative Force so that's also something that we're going to talk about in a little bit okay the next thing is sound so sound is um they'll try to connect it on the MCAT with um like hearing questions maybe some psychos questions where they'll um give you some examples and then you'll understand like oh you'll have to understand physics but you'll also have to understand some of the um some of the either like the biology or the biochemistry and that's kind of how they'll ask about sound so again sound is created by mechanical disturbances of in a material so you can imagine like when I'm creating friction you can hear some sounds and that causes oscillation of molecules in the material propagation is what I was showing you an example of and again sound propagates through all forms of matter but not through a vacuum and you should understand why it's not through a vacuum the reason for that is because sound needs all these particles to be moving and so if there's no particles in a vacuum then it's not going to move the next thing is that um sound is is fastest through solids than liquids and then again remember about this equation within a medium as density increases speed of sound decreases the next thing is pitch and Pitch is our perception of frequency so if I have a really high pitch um like my pitch is really high like I'm an opera singer then that's kind of how you interpret frequency of the sounds that I'm making okay the next thing is Doppler effect Doppler effect is actually kind of high yield you'll probably get at least one question about Doppler effect on your exam and um and the way that they sometimes test it is that they ask it in terms of radiology or they'll give you like a train and they'll ask you like how how can you interpret this and dopler is kind of when something is moving how do you interpret the frequency of that moving object and so let me see if I can find an example so this is kind of an explanation of Doppler effect and you can see that um this is one Observer and this is another Observer and this is the source of the sound on the ambulance and so this ambulance uh it's going to sound uh like this guy is going to experience a higher frequency of these sounds because the sounds are moving towards that person so because this P this ambulance is moving towards this person these sound waves are coming at this person uh and so it's going to this person is going to experience higher frequency whereas because these sounds are moving this way these sounds are going to be further separ operated for this guy and so this guy will experience lower frequency so even though the ambulance is just creating one sound the fact that this ambulance is moving but these two people are not moving and they're at different positions results in the Doppler effect and that's what that's what the Doppler effect is so how do we apply that here all you have to know is this formula which explains what the Doppler effect is and you just need to know what is the perceived frequency what is the actual frequency and if we have the actual frequency like if I told you the frequency of the sounds coming from the ambulance then you could tell me what the perceived frequency is for either person and all you would need to know is VD and vs so remember V is the speed of the wave the wav speed but then you need to tell me like what is the wav speed of the person who's hearing that wave and that's kind of how you figure out Doppler so this is a good um EXP explation of it so you can see that um F0 is the observer's frequency of sound FS is the actual frequency of the sound and then we have v v is the speed of the sound waves and then you have v0 which is the Observer so the um velocity at which the Observer is experiencing the sound and then we have VSS and VSS is the source velocity so this is speed of sound this is Source velocity so the sound of the ambulance driving this is the Observer velocity so what is the velocity at which the Observer is experiencing those sound waves this is the frequency at which the ambulance is making those sounds and then if you have all that information you can figure out what is the Observer frequency of that sound so this is a good place to understand Doppler effect and this is basically saying what is the Observer fre frequency of the sound based on the actual frequency of those sound waves so how we do this is we just take the speed of sound right the speed of the sound waves and then we add to it the Observer velocity so if the Observer is not moving then this is zero and then in the bottom we add to it the speed of the source velocity right and in this case this would be the speed of the ambulance so we do that calculation we multiply it by the frequency at which the sound is coming and then we get the Observer frequency of sound and that's what the Doppler effect is now it's important to mention that this is plus minus on the top and bottom and um the plus minus is coming from so if if the sound is going towards the person then you use the Plus at the top and you use the minus at the bottom and then if the sound is going away from them then you use the minus at the top and then the Plus at the bottom that's just something to no okay I'd recommend doing like a practice example with this and then you'll have it down um because it's kind of hard to just understand it by somebody explaining it okay then the next thing is intensity so intensity is just related to an amplitude so um if it decreases over distance and some energy is lost due to attenuation from frictional forces but it's just really important to know this equation um intensity is equal to power over area so the more power you have over the smaller area that's how intensity increases okay this is this is where we get more into the things that I told you I'll get into which is resonance and damping so um there's strings in open pipes uh and we can have closed pipes and open pipes so let's first talk about open pipes open pipes are represented by L equals this n * a wavelength divided two and N is just any whole number 1 2 3 then we have closed pipes closed pipes are represented by these this equation Lal n time wavelength divid 4 and you'll always have odd multiples of quarter wavelengths so it'll be like 1/4 of the wavelength 3/4s of the wavelength whereas these open pipes will be one half of the wavelength one of the wavelength three halves of the wavelength things like that and so this is basically describing the length of the pipe that'll allow for either an open pipe or a closed pipe and when I talk about open pipes you'll see that um closed pipes are closed at one end so it'll be kind of like um open pipes will be kind of like this or this or this right versus closed pipes will kind of be like that or that or that right it won't be the full wavelength it'll be a a quarter wavelength or a 3/4 wavelength and so that's kind of how you can think about open and closed pipes okay next I'd like to tell you about okay next let's talk really quickly about ultrasound so ultrasound are really cool devices they use high frequency sound waves and basically they send these sound waves and then they um are able to see when do those sound waves come back and based on that they can figure out density of tissues and they can figure out flow of blood within the body it's like science fiction things very cool and sometimes they'll use Doppler effect with ultrasound to kind of test whether you know Doppler effect um these are harmonics so as a shortcut if you see that the string is attached on both ends then you can kind of uh just use the number of antinodes and that'll tell you which harmonic you're looking at so this is the first harmonic this is the second harmonic this is the third harmonic um and this is kind of the wavelength that I was telling you about so again you can use this open closed pipe concept and figure out what is the wavelength so this is the wavelength is 2 L this is L over here and the reason why this is the wavelength is 2 L is because this is just half a wavelength so if you were to make the full wavelength it would go like that and that would be 2 L um this is just one wavelength right from one point to the same point on the on the next wavelength and then this is actually that's one wavelength and then this is another third of a wavelength um sorry that's another half of a wavelength so that's three three halves of a wavelength um and so that's why the wavelength is equal to 2/3 if you take the reciprocal of L um I told you that I would tell you about resonance and damping so the resonance is kind of when you increase the amplitude um by adding a natural resonant frequency so something that increases amplitude and damping is the opposite it decreases the amplitude because you're applying this damping Force so it's kind of in the name there okay the next concept is electromagnetic wave electromagnetic waves are um the what I was telling you about light these are transverse waves that consist of oscillating electric field and oscillating magnetic field so kind of has this um I'm going to show you an example so this is electromagnetic waves you can see that this is an oscillating electric field over here and then this is an oscillating magnetic field over here and so they're perpendicular to each other and that's why this is an elect electromagnetic field um okay so um the two fields are perpendicular to each other in direction of propagation of the wave then we have the electromagnetic spectrum and those are the range of frequencies and wavelengths found in the EM waves so this is the electromagnetic spectrum over here uh and you can see that it goes from gamma rays which are really really high frequency all the way to radio waves which are very low frequency High wavelength and in the middle there's visible which is actually a very small portion of this electromagnetic spectrum and that visible is just the things that we can see so I would know that um 400 is violet and 700 is red and these are the wavelengths in nanometers okay the next concept is hydrogen spectral Series so if you remember in the chemistry lesson there was kind of this whole um belief that you know um that there there's these there's this hydrogen at at and then around it there's these electrons and then based on where the electron um comes back to so let's say that we go from uh here let me show you an example okay this is a good example and basically um when an electron goes from a higher orbital to a lower orbital um or sorry I should say orbit when an electron goes from a higher orbit to a lower orbit it's basically releasing energy and so that energy comes off as light and that's light sometimes that we can see and so for a hydrogen atom they did these experiments and they found that when an electron goes to the first orbit from any of the outside ones it looks Violet and that's called the Lyman series and you don't need to know these names you just should probably know the color and then you should also be able to tell me why is that color the color that comes out and so anything going to the first orbit that's actually releasing a lot of energy and if you remember the really high frequency color is violet now going to the second is called Balmer and that's going to be like this bluish color then you have passion and then you have bracket and that's to the3 Nal 3 and that's to the Nal 4 so this is Nal 1 this is Nal 2 over here Nal 3 so this is four and then this is five and then if we go back we can kind of see what the colors are so Lyman is ultra Violet Balmer is visible passion is infrared and then this is kind of an acoustic love Speer pong Nal 1 2 and 3 and so the idea here is that when these electrons are going back to those shells or those orbits that's the color that's coming out okay then we have ride breakes formula and that's basically what I just told you and that's how you can figure out these colors because you take the N Final and the N initial so if we're going to one it's um if we're going to one the N Final is one if we're starting from two the N initial is two so this would be 1 - 1/4 and it would be 3/4 time this r value is equal to the frequency times this H value and then we can figure out what is the frequency of light that's being um uh emitted from the electron going from high shell to low shell okay um the next thing is defraction defraction is the bending and spreading out FL waves as they pass through a narrow slit and defraction can create this large Right light Fringe surrounded by alternating dark fringes and light fringes with the addition of a lens so it's helpful if I show you an example so this is defraction over here you can see that this person has this sight and then this this light kind of goes and bends around the slit over here and I think a better example would be right here and if you see that there's these waves coming in this way but then when it hits the slit it starts to defract or bend and that's what defraction is and the larger the the larger the slit the less bending that happens but the smaller the slit the more it kind of curves that way okay and you can see here wavelength is really really high with is much greater than SL slit length here and then wavelength is about slit length here and then wavelength is much less than the slit width here um and that's kind of how you can can imagine it okay this is a good example of what I'm saying so this is a small defraction effect and this is a large defraction effect and it's because this is a narrow Gap and this is a wide Gap okay the next thing is interference and this is kind of what I've already talked to you about which is that when waves interact with each other displacements add up and that's called interference now we have Young's double slit experiment and this is very very important so this is a good image I found on Young's double slit and essentially you send um you send these electrons here this is probably better you send these electrons into a double slit and then what happens is that it goes through both these slits and then those electrons interact with each other and they create this interference pattern where it's very dark in the middle but you can see that all these Columns of where the electron is hitting is surrounded by these light areas where there's no electrons hitting and you might ask yourself why is that happening and the reason is because these slits are um are like these electrons are interacting with each other and so when they interact with each other they're causing these little parts of Darkness but then there's also places where the the positive of this is interacting with the negative of this and they're interfering with each other in a way that there's no um no electrons hitting that area and so that's why you get these dark spots and light spots right next to each other and that's Young's Double slitting experiment so it says shows the constructive and deconstructive interference of waves that occurs as light passing through parallel slits resulting in Minima which is the dark fringes and Maxima which is the bright fringes then we have polarization so plain polarized light is that um it's kind of like when you're wearing these polarizing glasses and it only lets light through a um through if the fil through a filter if the electric field of the wave aligns with the openings of the filter so remember the electric field is kind of like in a certain direction and so the electric fields of the exiting light oscillate on the same axis and so this is an example of a plain polarizing light and so you have this light and it's going through but then this is the polarizer and it's only allowing these vertical lines to go through and so what you have at the end is just these vertical lines they only oscillate against this plane they don't oscillate in all the planes like this the circular polarized light is kind of the same thing it's the idea that um this is constantly rotating Direction so instead of this being a stationary thing it's constantly rotating like this and so you kind of have this very unique um pattern and so circular polarized light is created by exposing un unpolarized light to special pigments or filters okay um now we get to kind of like the the much harder things um these are things that took a long time to kind of understand so I'm going to go a little bit slower through this and so um making sure that we understand this so reflection is actually pretty easy reflection is just what you that's that's something you know when something goes in it reflects off an object and goes away and the important law of reflection is that this Theta 1 is equal to Theta 2 and this Theta 1 is called the angle of incidence and Theta 2 is the angle of uh reflection and you just draw a normal line to where the um to where the ray is hitting the mirror and then it reflects and that's how you find these two angles and the important law here is that these two angles are the same so that's what this is okay next you have spherical mirrors this is where it gets kind of harder so I would recommend just kind of memorizing this it's really hard to understand why it occurs but if you understand this and then you kind of understand this um then you'll be solid so let's start with this um when you have like these this object over here and then you have this Center of curvature and this object is further away from this Center of curvature what you end up with is this image over here which is kind of inverted and it looks smaller than the original object now when you have this object over here the center of curvature is actually way behind the mirror and so what you get is this virtual image this virtual image is much smaller than the original object and the focal point is all the way back here so here the focal point is behind the virtual image and it's also important to know that the focal point is in front of the center of curvature these are concave mirrors so concave looks like a cave these are convex mirrors convex is kind of like a v i don't know if that helps you but that's kind of how I think of it so concave is like you're looking at this and this is youu and then convex is this is you and this is the mirror so that's how you can think of it now now it's also important to know that this is a concave mirror right but then um uh you have to know is the object's position over here where it is right now and I'm talking about concave right now is the position over here or is the position over here because depending on where you're standing compared to the mirror it's going to change how the image looks so this is what took me a long time to understand but let's say that you're standing behind the focal point right then we have the real inverted because the object's position is greater than the focal length so just this is where we are this is where the focal point is and so because we are further away from the focal point it's going to be real and inverted now let's say that we're actually standing closer to the mirror right the object's position is less than the focal length so we're close standing closer to the mirror than the focal point what that's going to result in is it's going to be virtual and upright so actually this mirror our ref F flection will be upright it's no longer going to be inverted now this kind of makes sense if you think about it if you're standing really close to this mirror it's kind of going to look a little bit straighter versus if you stand a little bit further it's going to look a lot more curvy and so that's kind of why when you're standing Close to the Mirror you get a virtual and upright image because it looks a little bit straighter and so that's why you look you look upright versus when you're looking at it from afar it's so curved and then you look upside down so that's kind of how you can understand that and you can understand that now it's about convex virtual upright also one more thing I should mention is what is this focal point this focal point is the place at which these light rays um reflect and interact with each other so these light rays come and then they interact at this focal point so if you have light rays coming over here and then they interact at this focal point so that's kind of how you can think of focal point focal point is the point of focus of the Rays um okay Center of curvature is kind of like if you made this into a circle where would the center be okay now we have convex virtual and upright and smaller so fortunately for us it's kind of easy to remember this because there's only one thing which is that you're standing somewhere and no matter what you're just going to look upright and smaller so you're going to look like a small guy in this IM in this mirror reflection to you um the final thing and then it's also important to know that your focal point is going to be in front of the center of curvature okay the final thing is um the plane and this is just a normal mirror and so a normal mirror is going to give you a virtual image it's going to be upright and the same size so if you're just looking at a mirror it's going to be looking the same size as you and it's going to be upright so it's just going to look exactly like you and this is a virtual image okay and you can the a way that you can think of this it's kind of a little bit more complicated but they're kind of like spherical mirrors but they have infinite radi of curvature so what that means is that this is just like like this is like a a mirror but it's the radius is just infinite and so because of that this just becomes straight straighter and straighter until it's just straight and so that's a way you can think of it I never really found that helpful so I just think about that it's just a a plain mirror is just a normal mirror okay so I hope that helps with spherical mirror this is always really confusing to me okay the next thing is refraction refraction is um let's say that there's light Ray and it's hitting the water now this light Ray is actually not going to go straight through it's actually going to pass like a little bit um a little bit it's going to refract it's going to bend a little bit and that bending of light is called refraction now this is uh caused because of speed change and it's because light moves differently in in different different uh in different substances so in air it's going to move at a different speed than at water and so that's what um uh you you can figure out what the index of refraction is and by just figuring out what is c c is just three times whatever the speed of light in a vacuum divided by the speed of light in a medium and based on that you can figure out n which is the index of refraction okay now we have dispersion dispersion is just when various lights w lengths of light separate from each other so let me show you an example so this is dispersion of light it's just when you go through a prism or if you think about rainbows it's caused by dispersion of light through raindrops okay the next concept is Snell's law Snell's law is the law of refraction and remember when I was telling you about how light bends when it goes from air to water well now you can actually figure out mathematically what is the angle at which it's bending and that's a really helpful thing to know so basically what we do is we take N1 which is the index of fraction of whatever is the first substance and then we do N2 which is the index of ref fraction of the second substance and then we take the Theta of both angles and we can now figure out well if we have the Theta of one of the angles then we can figure out what is the bending of the second angle so it's important to know that this is measured from the normal so let's say we have light that's coming in this way and then it hits the water and then bends this way right so we need to to know that the angle that is the angle is this angle over here um and let me let me show you a picture so this is a helpful picture over here and so let's say that this is um this is the uh the light is going this way right I'm going to let that erase okay so let's say the light is going in this direction this way right um so first we take the we first we draw a normal line so this is a up and down line and then we have the Theta 1 which is this angle over here and then we have Theta 2 which is this angle over here then we should know what these two substances are this looks like water this looks like air so you'll be able to calculate N2 and N1 and we should they should be able to tell you like this is the angle at which light is hitting the surface and So based on that you can figure out okay this is what Theta 1 is now I should be able to figure out in which direction is the light going and that's what Theta 2 is so that's how you would answer Snell's law questions okay the next question is total internal reflection and this is just the law of reflection but this happens when light is moving from a medium of higher index to a medium of lower index with a high incident Theta so what is a high incident Theta well it's when the light has when uh the light when the Theta is really large so it' be like if this is the this is the surface and light is hitting like at a very steep angle like this way right in that case there might be total internal reflection where it just pops right out it's not even going to go through and it only happens when you have a medium of higher index of reflection to a medium of lower index of reflection so if N1 is really high and N2 is really low so N1 is high right and data 1 is high in that case you can just get complete reflection um and you might not even get any refraction at all you might not even get the light to go through so that's what total internal reflection is now we have critical angle and this is the minimum incident angle at which total reflection occurs and so if you just take this equation and then you plug it and you reformat it you'll get this equation this is the critical angle and so if the critical angle is for example 12° that says that at 12° or less or sorry at 12 degrees or greater you're going to have total reflection okay yeah so uh critical angle is the minimum incident angle so if it's like yeah again 12° it's going to be more like 80° if it's 80° or anything more than that then you're going to have total reflection that's an example of critical angle okay now we have lenses and lenses was also confusing just like mirrors to me so I'll try my best to explain this lenses again we have con X which is kind of like a I think of it like a v i don't know how you think of it and concave which is like a V which is like a cave that's how I think of it but yeah you just have to know concave is going in and convex is going out okay lenses is things that light goes through whereas mirrors are things that light reflects off of so lenses refract light to form images of objects and then we have thin symmetrical lenses which have focal points on each side so con let's start with concave because those are easier so this is a concave and if we send light into this then it's going to go outward right which kind of makes sense it's a cave so it's going to go outward now we have the focal length and the focal length is one half R right and um and we have F which is the focus and F big little f is just the length the distance from the focus to the mirror so this is little F and the focus is the big F okay so when you um are standing here or are standing here and you're looking at the at the concave lens you just end up with an upright image and it's virtual so this is this is the T and it ends up virtual and upright and uh when you are at a convex lens it's actually a little bit more complicated you have um a real real image or a virtual image and it depends on where you're standing so the way that I think of it is that if you're standing right over here then the image over here if you look at it will be virtual and ight but the image over here will be real and inverted and that's kind of how you can think about convex lenses okay the final one is lens maker equations and this is honestly not very high yield so I would just memorize this equation um but I wouldn't worry too much about it okay okay the next important concept is the photo electric effect and fortunately I've already talked about this so the photoelectric effect is the ejection of an electron from the surface of a metal and so when you um put light onto a metal so let's say this is like iron or something essentially there's going to be electrons that are shooting off and that's because you're injecting a ton of energy and so these electrons are now able to leave these metals and so if you want to figure out what is the energy of the photon of light these light you remember that light is has both particle and wav like properties and so you can figure out what is the energy in a photon of light and that is this equation uh it's just based on the frequency you multiply that by a constant and then you get the energy and then if you want to calculate the wavelength obviously then you can just do C equals wavelength time frequency and C is 3 * 10 8 that's the speed of light and that's how you figure out what is the wavelength okay the next thing is the kinetic energy and this is just for fortunately just the same formula so this is always a formula confuses people a little bit what is this W doing here what is that work and essentially it actually takes a minimum amount of work um or a minimum amount of energy from this light going onto the metal um to cause electrons to shoot off so if this light energy right here I'm going to use yellow here so let's say this light energy over here is too little energy you're not actually going to be able to eject any electrons so there's a minimum amount of work that it takes and that's what this W is that allows for a single electron to leave and so this W is that representation so you're taking basically the kinetic energy of the uh electrons that are leaving this metal you figure it out by taking that energy of light and then subtracting that work that it takes just to it just to get to that threshold so you can think of this work as the threshold that's necessary to eject any electrons so that's what this threshold frequency is referring to this work is uh in jewels and then this frequency is just in um in um one over nanometers that allows you to figure out or sorry um so yeah this is basically referring to the threshold frequency that's necessary to eject any electron from Material you can multiply that threshold frequency by this H and then you would get this work the energy and that's the threshold energy and so that's what this work function is referring to this H remember times the threshold frequency gives you the work and you can remember H is planks constant which is just 6.6 * 1034 Jew perss um and if you look at the units it kind of makes sense because you take this H which is jewles seconds and then you multiply it by frequen qu which is Hertz or one over second and then you get jewels which is the work unit okay the next thing is um bores model and uh this is just things that I've talked about before the absorption and emission of light so remember that U bore believe that they these electrons live in stable and discrete levels and so when you go from one level to a different level you're either releasing energy or you're absorbing energy you absorb energy when um you're going up a level and you're uh releasing energy when you go down a level closer to the nucleus the absorption is what I just mentioned same with the emission so emission happens when you go down a level and because of that you're emitting some energy and usually that energy or I should say that energy is represented in photons of light so remember when we were talking about all the different colors of light that happens like ultraviolet or red that's because these electrons go down in or a level and then you release this color of light okay now you have absorption spectra and then you have fluorescence so fluoresence is just when a species absorbs high frequency light and then returns to ground state in multiple steps so um instead of it going down all at once it just goes down in different steps and then each step has less energy than the absorbed light and is within the visible range of the electromagnetic spectrum so imagine that I shoot a ton of light into this um into this atom this elect jumps into like the fifth level and now one by one it's going to the fourth level then third level then the second level that's what this fluorescence is referring to okay the next thing is nuclear binding energy and mass defect the main thing to know about nuclear binding energy is that it's really it has a lot of energy so it takes a it there's a lot of binding energy that's um connecting these nucleons nucleons are protons and neutrons and essentially that's just because those are within the nucleus now there's four fundamental Natures forces of nature there's what we talked about gravity there's electrostatic forces and then there's strong and weak nuclear forces and those just refer to these to these nuclear binding energy the forces between protons and neutrons okay now there's Mass defect and this is just the difference between the mass of the unbonded nucleons and the mass of the bonded nucleons within the nucleus the unbonded actually have more energy and therefore more mass than the bonded constituents it's kind of interesting why there's this difference in Mass when like a proton and a neutron are right next to each other versus when the proton and neutron are separated and so actually when these things are separated they have more mass and more energy slightly more mass a lot more energy and because of that the mass defect is the amount of mass that's converted to energy during nuclear fusion nuclear fusion you should also know what the difference between nuclear fusion and fision is which is what we'll get into next okay um so I just mentioned fusion and fision so Fusion is when small nuclei combine into large nuclei and then fision happens when large nuclei split into smaller nuclei so this is fision and then this is Fusion okay um uh the next thing is energy is released in both fusion and fision because the nuclei formed in both processes are more stable than the starting nuclei so the reason why Fusion INF fision happens is because the end product is more stable so maybe in the fision process this large nuclei is very unstable and in the fusion process these small nuclei really want to combine into this large nuclei okay the next thing is radioactive decay this is pretty high yield as well and there's three types of particles that you can lose from the nucleus or I should say four types of particles that you can lose from the nucleus one is this beta which is essentially just an electron another one is this which is just essentially um like a positively charged with no Mass particle so one is just uh you're losing something that has no Mass but has a negative charge another one is you're going to lose something that has no Mass but has a positive charge another thing is that you're just losing energy so you're not actually losing mass and you're not losing charge it's just gamma and then the last thing is kind of like losing something that has four mass and two plus charge um kind of like a helium uh particle but it has two plus charge okay so alpha particle is again that's what they're comparing it to like a helium particle uh which is basically a helium nucleus so if it was a helium atom without the electrons that's what an alpha particle is and so that's when you can see in alpha decay basically you result you go from one atom to another atom and the atom is losing four in its mass and then two in it charge and you get an alpha particle the betag negative Decay is kind of like a neutron converting into a proton because you're losing a charge right and so when you're losing a charge but you're not losing mass it's kind of like a neutron is converting into a proton that's kind of a way you can think of it so that's what this is showing then you have beta positive Decay and that's kind of like if a proton became a neutron it's like the opposite of this um because protons and neutrons have the same mass but different charges that's what this is showing and then finally we have gamma and Gamma Decay is just you're losing a lot of energy which is represented in photons um and so you get like a lot of light that's leaving and that has very high energy so this is basically you're just going from a very high energy nucleus to a lower more stable energy nucleus okay now we have electron capture an electron capture is just imagine that there's these electrons that are in the orbit and now the nucleus is just going to absorb or capture this electron and so that's what this is showing is that we take an electron from the inner shell and then that's we end up with this um so we end up with the nucleus now having one one negative charge um so the charge is decreasing by one now halflife is pretty high yield you'll probably get one question or two about half life and it's the amount of time that's required for half of the sample to Decay so if I have aund of I don't know radon and then it becomes 50 um in like one week then the half life is one week if it becomes 25 in two weeks you should know that the half life is one week because there's two um two times that it haved one's from 100 to 50 and then one's from 50 to 25 so if it took two weeks that means that one week is the halflife uh this is the equation for exponential decay uh over here and it's it's pretty important that you know this so it's just the number of undecayed nuclei um and then this is the number of UND decayed nuclei at time T equals z and then we have an a known Decay constant and this is just dependent on what what like radioactive material we're working with and you'll actually see this in um like I was doing a rotation with radiation oncology and some of the medicines they used they they had radioactive half lives and so for the doctors to prescribe these medicines to the patient they kind of had to know like what is the time of delivery of this medicine and how much do we have to prescribe to make sure that this patient will be able to take off with this medicine so um that's kind of like a clinical correlate that you might see when you're taking your MCAT okay um next is just this is just the image that represents everything I was talking about and the these might be able to help you understand what's going on but I think you probably get the gist of it okay I'm going to go really quickly through the math because I think that you uh probably know almost all of this already so let's just go through it just to make sure you know it so you'll know what scientific notation is it's like when you use this one digit and then you multiply it by um 10 to the power of something and that can kind of help you add multiply subtract um divide things like that um there's this Lars pneumonic I've never really found it that helpful but some people like to use that Lars left add right subtract when they're doing this and then there's significant figures so significant figures is when you include all non-zero digits and any trailing zeros in a number with decimal points okay um in the in the MCAT it's important that when you're doing math you should just kind of be good at estimating um you don't really need to be able to do a complete math with all the digits and numbers and all those things so just get good at estimating things because that'll speed up time significantly now trigonometry is not really that high yield but it is kind of helpful to know like s cosine Theta uh s cosine and tan so s is just the opposite over the hypotenuse cosine is the adjacent over hypotenuse tangent is the opposite over the adjacent so just make sure you know these um and then um if you know this and that's great if you don't know it I wouldn't spend time memorizing it it's not too high yield I would just know that um at zero what are these and then I'd know probably at like 90° what are these and that's going to be probably the two most high yield values that you would need to know um okay next we have logs so you're not going to need to know logs too much um they might ask you to like to take logs for halflife or um different types of exponential decay type questions so I would just know logs based on that um I would try to kind of get good at like okay if log of log base 10 of 100 is two then can I estimate what log base 10 of like 356 would be like is it closer to two or closer to three or what would it be like like that is kind of the extent of which log you might need to know and then I would kind of know like how to manipulate logs a little bit but again it's not that high yield okay um kind of be able to estimate like oh is the square root of8 like what would that kind of be close to um things like that but again it's not too important I think most of the math that you'll need to know for the MCAT you'll kind of get through practice questions and you'll kind of get the idea like you definitely don't need to understand this whole unit circle um especially if you don't recall it from like Algebra 2 trig or uh calculus or whatever like it's not super important that you remember 135° is this value um it can help you but I wouldn't waste too much time on these things okay again we'll go quickly through this so the scientific method you've learned um at nauseum several times you know that you have to formulate a hypothesis test that hypothesis and then provide results for further testing um ethics so you should know that medical ethics there's four like huge tenets of medical ethics you're going to be uh it's going to be helpful in like interviews and when you start like clinical rotations in med school to know these four uh tenants which is beneficence do good to your patients non-maleficence don't do any harm to your patients respect your patients autonomy so like respect their decisions when they're capable of making those decisions and then Justice is was always the hardest one for me but Justice is basically you have limited resources as a clinician so how are you going to decide how to distribute the resources that you have for the patients that you have research ethics um essentially is pretty similar you just have to have respect for people resources making sure that you do good by people um and then this is kind of an important point which um I learned about a lot more recently in college which is that um when you're doing a lot of these clinical trials um your ethical responsibility is that uh if you're doing like a um if you're giving like two different types of treatment like treat a and treatment B for um a population like let's say that you're treating cancer patients and you want to figure out like is this medicine good or bad and you're giving that medicine and then you give like the standard treatment and you kind of compare the two samples the moment that you realize that you know one treatment is better than the other you're ethically obligated to um kind of like stop the experiment or to make sure that the patients if especially if it's going to extend their life or stop them from dying you're not allowed to continue giving them an inferior treatment um just because you want to like like complete the study um because that's kind of against ethics uh and you can read more about that I'm kind of um summarizing it and not doing the Justice to it but that's kind of the main idea of research ethics okay research in the real world so you should know populations all the individuals samples is just subset and uh sample data is called statistics you have internal and external validity so internal validity is this is this experiment like uh correctly done like is the dependent variable the result of manipulating the independent variable or are there confounding variables that the researchers haven't accounted for um external validity is like can this actually be generalized to the main population so if I do a study on smokers but then I say like oh exercise is good for everybody um but I only did this study on smokers and that kind of has low that statement has low external validity because I've only done the study on a specific um subset of the population uh within subject design it's important to know that so controls for individual variation um and then we have statistical significance so what is the chance that this result is due to chance there's always a small percentage likelihood that like the differences and the clinical outcomes is just because of chance and so we want a high statistical significance um so that we know like oh this is probably because of the differences in the independent variable not because of chance um clinical significant so like how important is it for patient outcomes um it's important to know like moderator variable mediator variable dependent variable and hopefully we just get independent variable that affects the dependent variable okay uh we have basic science so you have variables independent dependent variable we have positive controls negative controls positive controls ensures that the change in dependent variable occurs when it's expected and depend negative controls occurs when there's no change in the dependent variable when none is expected um I'll try to think of an example and then show you okay this is a good example of positive versus negative control so let's say my um experiment is I give some people orange juice and I give other people no orange juice and then I see like what is the difference in their um sorry um let's say I give some people water and some oh sorry some people no orange juice and some people orange juice and My outcome is I want to measure um their vitamin C levels at the end of this or I want to see like which patient population has more scurvy um so you might say like okay um well orange juice population is going to have more uh vitamin C at the end of it but then what if it's because of something else in the orange juice or something that we're not accounting for like what if the people who are having orange juice or just in general like I don't know going out in the sun or having more leafy vegetables or something and that's resulting in the thing so then you have positive controls and negative controls so positive controls you give some of the patients vitamin C and you see like oh is that actually resulting in what I want it to result in and then you give some a negative control which is like I give them water and then I see like is that resulting in what I'm expecting to and so as long as the positive control results in what you're expecting and negative control results in what you're not expecting you're increasing the internal validity of your study okay um now we have accuracy and precision um I'll show you an image of this so this is accuracy versus Precision this is also kind of high yield um this is high accuracy low Precision this is low accuracy High Precision so accuracy is how close do you get to the Target Precision is how close to the dots the different trials get to each other okay um next we have human uh subject research so you have cohort studies you have cross-sectional studies and then you have case control studies so make sure you understand the difference between these um cohort studies is you look at it throughout time you look at a cohort throughout time and then you assess the rate of a certain outcome so um let's say I look at a ton of smokers over time and I see like how how many of them do do get like lung cancer different types of cancer cross-sectional studies is I look at a single point of time and then I'm figuring out like how many of these people have been smokers and then how many of them have uh cancer at the moment uh and then you have case control studies so you look at some people who um are in one uh group and then you basically sorry you look at the outcome first so you look at um okay how many of these people have lung cancer at this moment of time and then based on all the people who have lung cancer then you go back and then you look at their charts and look at how many of these people have exposure to smoking and that's kind of like a case control study Hills criteria uses uh figures out if causality can be supported um this is not too high yield I wouldn't uh spend too much time on this but biases is pretty important I would understand biases so you have selection bias detection bias Hawthorn effect social desirability um bias I'll start with Hawthorn effect that's just if you're being observed you probably will change your behavior if somebody was watching me how how many times I'm exercised in the week I'm going to exercise more just because I know I'm being watched selection bias is like the idea that I'm choosing people who are different from the population in uh clinical trials you have a lot of selection bias a lot of times because a lot of the people who are um doing something are usually like volunteers for those experiments or people who are getting paid some money and so that chooses maybe some specific people that are different from the population detection bias is from the educational professionals that are using their knowledge in a way that's inconsistent and by searching for an outcome disproportionately so if I gave like pathologist a lot of slides and I told them like figure out like how many of these people have um lung cancer or something and uh I told them like oh all these people are smokers and this this pile all these people are not smokers like maybe there's some detection bias over there and then there's social desirability bias so if I ask like everybody who has lung cancer like how many times have you smoked in the past there's some social desirability to say like oh I haven't really smoked in my life things like that placebo effect is theide a that uh results are influenced by the fact that subjects are aware whether or not they're in the control group so you want to make sure that they're blinded to it so make sure that they don't know whether like the pill is a placebo or whether the pill is um you know whether they know whether they know like the pill is like supposed to have some effect or whether they're just not receiving a pill so just give them like a placebo pill and don't tell them like oh is this uh tell them like this might be a placebo pill or this might be the pill that we're hoping will have an effect um confounding variable that's an extraneous variable that affects both the dependent independent variable you have mediating variable which is over here which is like a middleman between the independent and dependent variable and then you have moderating variable which influences the relationship between the independent and dependent variable okay now we have measures of central tendency so we have mean median and mode um this is really important it just means that you need to know mean is the average median is the middle of the data set mode is the most often data point normal distribution the median and the mean are the same so is the mode um you should know these standard deviations and the amount of the percentage of the population that exists Within These standard deviations so 68% in the first standard deviation 95 in the second and 99.7 and the thir there's also standard deviation um in a normal distribution the mean is zero the standard deviation is one in a skewed distribution you can have left skewed or right skewed this is um they like to test this sometimes so you they can test median and mean so just know like left skewed um there's like a long tail on the left and right skewed there's a long tail on the right and so left skewed the median on the sorry the mean is on the left and the left skewed and the mean is on the right and right skewed now there's bodal distribution that means that there's multiple Peaks um and so you can get like um yeah you can have multiple peaks in a bodal distribution there's measures of distribution so range is the difference between largest and smallest there's inter quartile range which is the third quartile and the first quartile so 25th percentile and 75th percentile standard deviation is the measure of variability around the mean and then outliers is anything that's more um than three standard deviations away from the mean so that can be above or below um yeah these are the relationships so this one over here this exponential then there's logarithmic then there's quadratic and this is curval linear it's just quadratic of side down um you have probability independent events is like flipping a coin twice it doesn't affect the probability the second time dependent events it does affect the outcome of the other events terminology is mutually exclusive means that you cannot occur simultaneously and when a set of outcomes is exhaustive then there's no other possible outcomes so mutually exclusive like getting a heads inails when you're flipping a coin that that's mutually exclusive and then when there's a set of outcomes that's exhaustive then there's no other possible outcome so when I flip a coin uh twice I can get two heads two tails one head one tail or one tail one head that's an exhaustive set of outcomes statistical testings there's hypothesis test um we want to figure out whether the null hypothesis can be rejected P value is how we do that there's a significance value usually significance value is 05 which is that we're allowing 5% um probability that the outcome Can Happen by chance and then P value is what's the probability that this outcome happened by chance so the P value is like 0.1 that means that there's a really small likelihood that the outcome happened by chance it means that we can probably reject the null hypothesis confidence intervals just tells us about the range of values around the sample mean so usually we use a 95% confidence interval it's important to know um type one and type two errors type one error exist over here and type two errors exist over here so type one errors is um uh let's see in this example they say passenger safe passengers uh potentially dangerous passengers innocent pass passengers Not Innocent so in a type one error you say it's a false hit um you assume that they're potential you assume that they're dangerous but they're innocent and then type two error um is a false Miss let me find a better example for you okay this is a good example over here you can see that there's a Minor's decision of an actual emergency so if there's an actual emergency then you get a yes a hit and if there's no emergency the minor decides no then it's a correct rejection but a type one error is that the minor decides to panic even though there's no emergency a type two error is the Panic minor decides not to panic even though there is an emergency so that's like a false alarm versus a a false a Miss um so we call this type one error false alarm and we call this type two error a Miss otherwise it's a hit or a correct rejection okay um finally we have charts graphs tables and this is just Pi um Pi or bar charts which is for categorical data histograms and box plots as numerical data and then linear semi log or log log plots you can use by distinguishing the axis and usually this is just used for convenience to kind of the log log plots to kind of um show the data in a more presentable manner slope is obviously the rise over the run so the the change in the Y over the change in the X and that's all of the physics and math that you need to know for the MCAT um I hope this was helpful thanks so much for watching and I'll see you in the next video bye everybody