Transcript for:
AP Physics 1 Exam Comprehensive Review

hey everyone welcome back to another video So today we're going to be going over the AP Physics 1 exam review for kinematics so this is going to cover everything you need to know uh for the exam in terms of kinematics and this includes projectiles and I have a couple other videos that have questions that range in difficulty from easy to hard um so after this one after reviewing all the content I suggest you try those questions um so let's just get right into the so the first thing we have to recognize is just some basic things regarding uh physics foundation and so we need to be able to recognize the difference between a vector and a scalar so vectors have both magnitude or or size and a direction um so example of that would be displacement velocity momentum now scalars are quantities that only have magnitude and so that's stuff you don't have to specify direction for like Speed Energy distance um so now when you're adding these vectors there may be some problems that show up in terms of testing your knowledge on adding adding vectors you need to add vectors from head to tail and also include the direction and the more important part of vectors um in terms of the actual exam is being able to break them apart into components so once you break them apart into components you want to use the pagon theorem um to analyze it so here's an example let's see we had a ball that was long launched with 20 m per second of initial velocity because the force of gravity is acting upon the Y Direction but not the X Direction it affects it differently so in order to analyze its motion what you need to do is break it apart into its components um you know the angle measure presumably and then you can just use tra to find the different velocities uh just like that all right so now let's get into some of the actual motion stuff for kinematics so the first thing is just which is represented by D but sometimes it can just be written as um D for displacement like this so sometimes you can write displacement like that with um like that um but more traditional way to represent displacement is just D with errow over it to show direction so distance is scalar well displacement is a vector and that represents change in position right so that is otherwise known as final position vers minus initial position uh so easy way to think about that is let's see he had a guy and he walked forward 10 steps and then walked backwards five steps his total distance traveled would be 15 Steps but his displacement which is change in position would be five steps um speed is distance over time velocity is change in position over time or displacement over time acceleration is just how fast you're your velocity is changing over time and there are the different units which are represented as m/s for velocity and m/s squared for acceleration um motion graphs you need to know how to interpret these graphs and I just have one example here um where you can see the position is exponentially increasing right um so in contrast to that you have that velocity over time graph that's going to uh be increasing at a con Conant rate and so because you're increasing your velocity each increment of time what you're going to get is the exponentially increasing position right you're getting faster each time and therefore your position is going to change exponentially now your acceleration is based off your velocity verse time graph just like your um velocity is based off the position over time graph and that represented by the slope so the slope of the position versus time graph is your velocity the slope of the Velocity versus time graph is your acceleration and then you want to work backwards from that which is analyzing the area under the curve so the area under the curve for as acceleration would be change in velocity and the area of velocity over time uh would represent your displacement all right so here's another thing you might want to take note of which is the dot diagram so being able to differentiate between um the position of an object whether it's speeding up or slowing down so let's say you had like a motion camera that captured the position of the object um every increment of seconds like every 1 second um so you need able to tell whether it's speeding up or slowing down so the first example you can see how it's speeding up because um since it's going faster right um in that same amount of time when it takes that picture um the distance it travels is going to be greater and in contrast when it slows down that distance is going to decrease okay so now we want to look at the kinematic equations and these are the uniformly accelerated motion equations and so you want to use these when the acceleration is constant if acceleration isn't constant what you can do is just break the problem apart to analyze it in Parts where the acceleration is constant so the first three here are on your reference table um but the two in green are not and those would probably be helpful to memorize um so what you'll find is that two and five are pretty similar in terms of uh the content the only difference is that the uh initial vossi is swapped with the final velocity um and to make up for that instead of + 12 a t^ 2 it is- 12 a t squared and another thing thing to know about these equations is basically if you have a unknown variable and you know the other three or two variables then you can plug it in to solve for those and that is sort of the basis of kinematics and X in these examples can be interchangeable with Y it just shows the uh plane that is being analyzed and you'll see it in the practice problems now we want to look at freef fall so this is when you just throw an object into the air and then you want to analyze its motion or let's say You Dropped a ball from a cliff um so this is where the only force acting upon that object is the force of gravity and we're ignoring air resistance um and the acceleration due to gravity on planet Earth is 9.8 m per second squared it really is 9.8 m/s squar but because it's acting downwards it's NE little G um so these are the motion graphs for it you can see how um let's look at this first one where there is position over time this is something that would be represented by let's say you throwing a ball straight up and then it comes down so you throw it straight up and then it reaches its apex and then comes down to its initial position and that the velocity over time graph you can see is where you give that ball a initial velocity but then what happens is that since the only force acting upon it is negative G right the acceleration is going to be um sorry that velocity is going to be positive but it's going to be decreasing right until it reaches zero which is when it hits its apex and then it's going to go negative and start falling back down you can see how the areas are equal to each other so this area right here is equivalent to this area right here which shows the total change in displacement which would be zero if the ball came back down to you and then the acceleration to the gravity is the only force acting upon it and that's why it's just a straight line in the negatives which shows it's being being affected by that um 9.8 m/s squ all right so the other thing regarding freeall is up and down problems and so we already talked about that symmetry that you're going to see um but there are two strategies you want to use when analyzing these problems you can either analyze the whole motion which the displacement would be zero because it came back down um the velocity just before landing is the negative of that initial velocity and then the times just the toal time it took for the entire motion or you can just analyze just the up portion or just the down portion in which the uh displacement would be Max the velocity would be zero since when it reaches its apex that would just stop um and then time is just half the time all right so the final thing we're going to cover is projectile motion in terms of kinematics um so there are two types of projectiles you're going to have angled projectiles and horizontal projectiles so when it's angled it's launched at an angle into the air and when it's horizontal it's just launched at 90° flat given an initial velocity as well and that initial velocity is going to act um in the X Direction um so these are a couple uh universal laws that would apply to these projectiles so for the angled projectiles um what you're going to do is break that velocity into its component right just like what we uh said before we want to break that initial velocity right here into its different components using trig um so once we get those values there are a couple ways to analyze it and I'll get into that in a little bit but now we'll to look at the um horizontal projectiles so your initial uh acceleration in the X direction would always just be zero right because after you give it the initial velocity um there's nothing acting in the X Direction since sum of all the forces in the uh X direction would be zero when it's in the air however the acceleration in the y direction would just be the force of gravity at negative little and another thing to note here is that when you give it a greater uh velocity in the X Direction it would not affect the flight time it only affects the displacement in the X Direction and the thing that affects time or flight time is the a velocity in the y direction and so when you get comparison questions about how long it taking things like that or drawing graphs that's something you want to take note of another thing is that time links the X Plus y directions and so when you draw times table like X and Y in order to see what variables you're missing what you can do is find time using one of the either X values or Y values with the uniformly U accelerated motion graphs and then you can use that to find um the missing values for the other side in order to get your answer um just a little uh breakdown of the different ways you can analyze it when this angled projectile comes back down to its initial uh y position like we said before with the up and down problems the uh final velocity would be the same as the initial velocity but negative times total time and then the displacement would be zero now when you want to analyze it as it goes to its Max height um it reaches its apex and so it's zero for a moment there in terms of velocity times half the time and the displacement would be Max so that does it for the AP Physics 1 review for kinematics um there are going to be some question questions uh linked above somewhere so I would recommend you guys check it out and thank you for watching hey everyone so today we're going to be going over the Dynamics review content for AP Physics 1 and this is for the exam um so yeah let's just get right into it so the first topic that you sort of need to know is just to have a feel for free body diagrams right so you kind of have to know what all the forces are so the force of gravity is very common and applies to pretty much every single object so FG where the force of gravity is equivalent to the mass times the gravitational constant and it always points points straight down towards the center of Earth now granted you're on Earth um there's force of friction which is parallel to the surface and opposes motion there's Force normal which is the force acting on the object by the surface and it's going to be acting perpendicularly away from the center of mass of that object and then there's tension force or applied force um so that's basic basically where the force is pulling the object by a chain rope um or anything of uh those means so here's an example uh very simple it's just a block with a mass of 2 kg is pulled to the right by 5 Newtons of force at a constant velocity and you want to draw the free body diagram so to draw the free body diagram obviously you just draw arrows from the center of the mass um it's given that it's pulled right by 5 Newtons so that's what we did and because it's moving at a constant velocity that force of friction has to be opposing it in the X Direction at 5 Newtons as well um and we'll talk about it later in terms of Newton's Second Law and then it's not accelerating in the y direction and therefore we know that the force normal is equivalent to FG all right let's move on to the Newton's first law so Newton's first law states that a object at rest remains at rest and if it's in motion it will remain in motion at a constant velocity unless it's acted upon by a net external Force so in this example you can see revisiting that block where it's 5 Newtons of force of tension and then 5 Newtons of force of friction that object is either going to be at rest or moving at a constant velocity because net force is zero and you can tell the difference between those whether it's at rest or moving um by the type of friction so it's either static or kinetic friction and we will talk about about that later on over here with this chart but let's move on to new Second Law which is sort of like the inverse of um new one's first law and that's where you do have a net force so a net force will cause acceleration in the same direction so it's basically a equation right so we know that net force is equivalent to masstimes acceleration and whenever the net force increases um acceleration will also increase at a constant direct relationship granted mass is constant and then as for Mass if mass increases and the uh net force stays the same then acceleration will decrease inversely okay so now let's talk about nuan's Third Law so basically uh new's thirdd law states that anytime two objects interact they're going to experience the same Force which is equal and opposite um so the force experienced by one object on the other one is the same except it's opposite um from the other object to the original one so here's a little example so let's say I punched a wall with 10 Newtons of force right so the force of the wall on my hand is also going to be 10 Newtons except it's going to be acting towards my hand and so it's going to be acting um in the left right we Define the left as negative and that's why it's equal and opposite all right so let's now talk about friction so the first thing I want to touch upon is static versus kinetic friction so we have this chart here which uh shows that over the uh over time as force is applied um the static friction is the first one which pops up and that is where friction hits a Max right because that's the amount of force that it takes to get something moving against friction but once you do get it moving now you're going to have kinetic friction which is the friction that opposes the object when it's m moving so static friction will always be greater than kinetic friction because it takes more uh Force to get something moveing then to continuously uh have it move after the initial Force so another thing to know is that force of friction is equivalent to Mu which is the coefficient of static friction but the equation is interchangeable with ktic friction and the problem will usually tell you um which one it is times Force normal so the coefficient is a property so it tells us how rough the surface is it ranges from 0 to one with zero being frictionless and you can only change it by changing the surface another thing to note here is that if the object is not accelerating in the y direction then FN is equivalent to FG and so that means that if you have greater mass there's going to be more force of friction all right so components of vectors so this is where we talked about this in like kinematics the kinematics review um so after this video If you haven't seen a kinemax review I would highly recommend you check that out as well um so this is where let's say you had a sled right and you pulled it at an angle that force of tension is not going to like act equally and so in order to observe the effects of the force you have to break it apart into its components and observe it in the X and Y Direction so you can see here in order to do that you would have to Theta the angle that's pulled at um or the angle that the force makes with the horizontal and then you can just use trig in order to find each of those uh values and I have a little example here showing the net force right so the net force in the X direction is just that a component of Ft in the X Direction plus the force of friction and the force of friction is negative that's why it's negative FF and in the y direction it's Force normal acting in the positive because it's going up and then that force of tens y um plus FG and FG is negative because it's acting downwards which we Define as negative all right um I think the next thing I want to go to is actually elevator problems so the elevator problems a pretty simple topic but basically what you need to know is that when you step on a scale it's reading the normal force um so what this means is when you step on a scale um let's say on Earth versus on the moon that's going to be different right your mass is different from your weight so because of this let's say you're on an elevator and it's accelerating in a certain direction then that means according to Newton's Second Law there must be an imbalanced force and so the force in the direction of the acceleration must be greater because there's imbalanced Force right to cause that acceleration so let's say I have this guy here in this elevator and the elevator is accelerating upwards so this means that the imbalanced force here would have to be FN so FN has to be greater than FG and when I put into the equation the net force acting the Y would be FN as the positive and then plus FG and then I would set this equal to M mass time acceleration and then you'll find that FN will indeed be greater than FG all right so the next thing I want to do before we talk about forces on an incline is systems so there's no like specific thing for systems but these are just a couple uh key takeaways I would definitely note about systems cuz this is a pretty big topic and the majority of forces problems are probably going to be observed through A System's lens so it has to deal with interactions between multiple objects right and for AP Physics 1 um strings and Ma and pulley are massless and a couple key pointers is you want to observe systems as one object accelerating so you can sort of like take away the internal forces and then just observe the outside forces to see um what's affecting the system and then zoom in on that one object um you want to label the forces that are trying to accelerate versus uh trying to stop the system from accelerating so that's that looking at it from lens of the system and you also want to use some of the forces equals ma for the system because um in most cases when an entire system is moving as a unit um the acceleration in the system is equivalent to the acceleration for a object in the system so once you find the acceleration in the system you can then use nap Force equals Ma so new Second Law to find the sum of the forces and then uh some of the forces for like the object and then you can just plug it in for some of the forces of the object equals the mass of the object time acceleration in order to find string tensions uh other forces acting on the object Etc so here's a little uh practice problem so we have the system here of two blocks and they're connected by a string so it's accelerating downwards because of that 5 kg mass and then that 2 kogam mass is just on the table and so when we observe it from A System's perspective the that force on it is just the force of gravity acting upon that 5 kg Mass so the force of gravity would just be 5 mg right mg so 5 * 9.8 = 49 Newtons internal forces of force of tension cancel out and then the mass of the system would be the total mass so we have the 2 kg and the 5 kg and so we can calculate that the acceleration is 7 m/s squared and since it's moving as a unit that's the acceleration of the system and the object inside and so now we can just calculate the force of tension by looking at the first object so the first object some of all the forces is that force of tension because the force of tension is the only one acting upon it in that direction there's the force of gravity and force of normal force but those are equal because it's not accelerating um up and down that is so some of the forces equals Ma so the mass of the object is 2 kg cuz we're only looking hand it from the lens of observing one object and then the acceleration we already know of the system is 7 m/ second so for the object it must also be 7 m/s squared 2 * 7 is 14 Newtons and since we know that the only force acting the xtraction is a force of tension that force of tension must equal 14 Newtons now let's look at forces on an incline so whenever you have like a block on an incline or just any object you can break Force gravity into its components where you have to because uh very similar to where that force of tension was acting on like the sled problems um it acts on X and Y differently so we call those directions FG perpendicular for the Y and FG parallel for the X you want to use trick to to find the magnitudes and here's a little proof to see which angle in that right triangle you create is actually Theta so just a couple things to note for the block when it's in like equilibrium is that the Su of the forces in the x is zero some of the forces in the Y is zero and therefore um the forces acting those directions are supposed to be equal to each other so force of friction that static is going to be equal to the FG parallel component as you can see up here um where the forces are acting in the direction so of FG is acting in X FG perpendicular is acting in the X FN is acting in the Y and FG perpendicular is acting in the Y um so here's a problem solving tip me the coefficient of static friction or kinetic friction sort of links the X and Y directions so force of friction over FN equals mu so if you know two of the variables you can just solve for the last one for force of friction we know x and x and force of force normal Xs and the Y and so that's sort of that link um whenever you have a problem that's asking for one of those variables and here's another thing where force of friction kinetic if it does note that means that the object is moving at a constant velocity right and here's another thing for when the object is not uh at equilibrium so when it's accelerating um so here the problems can vary so these are just very general guidelines you want to follow and you want to adjust it based on the problem so usually net force in the Y will be zero because it's not going through the block right and when it does accelerate that's usually means there's a net force in the X Direction and so usually what that means is if there's not a rope or tension or something then FG parallel will be greater than a force of friction which is causing that net force and therefore causing acceleration so yeah that does it for this review for AP Physics 1 for the Dynamics unit and thank you guys for watching everyone so today we're going to be covering the circular motion and gravitation content on the AP Physics 1 exam uh so the first concept is uniform circular motion so essentially whenever you have objects that are moving in a circle um in order for that to happen you're going to have what is called a centripetal force um so they're going to have a change in Direction they're constantly changing direction and therefore their velocity is always going to be changing um and that requires a force right but just because their velocity is changing doesn't mean that the magnitude of the Velocity which is speed uh changes as well so the speed does not change and instead stays is constant so what is a centripetal force so a centripetal force is going to be a net force right because it's derived essentially from Newton's Second Law a net force will cause acceleration so the centripetal force is the net force that is responsible for keeping an object in a circle so whenever you have net force there must be acceleration right so here is a example of that we have a ball in uniform circular motion and basically what you're doing is you're just swinging it on a spring on on a string uh vertically right and then when it's at this moment we've captured it uh the net force on it is going to be FG the force of gravity pointing straight down towards Earth and then the force of tension also pointing straight down because uh the ball is at its apex right now so we Define the center of the circle as positive and away from the center or outside of the circle as negative so in this case the net force would be FG plus ft um and what you'll find is that your net force uh will always be the greater value because that is the direction um in which the acceleration will Point another thing to note here is that when you're writing out the centripetal force it is expressed as AC or rather v^2 over R all right so that is the important thing to note there about uh notation wise of equations and here are a couple guidelines when drawing those diagrams so for free body diagrams you're not going to have any new forces however there are some slight adjustments and caveats you want to take into consideration so the net force like we talked about will always Point towards the center of the circle the velocity is tangent to the circle the acceleration is just how quickly the velocity changes that's AC there's no Force if it asks you to draw a free body diagram you're not going to be drawing the velocity or the acceleration on there obviously and the speed stays the same so there is this thing called critical velocity so critic IAL velocity is basically the minimum or maximum velocity you need to either make it through a loop or to go over a hill or stay on a Surface um essentially this is where you're going to be setting the normal force to zero um and then solving for velocity there so usually it's going to involve some sort of contact like a car on a hill or a car on a surface or something um so that's just something to know about critical velocity all right so the second thing is gravitation so essentially objects are going to be orbiting a shared Center of mass and the first part of this is Newton's law of gravitation so it's very similar to Newton's third law actually you can see here that the gravitational force that planet one exerts on Planet 2 is equivalent to the gravitational force that Planet 2 exerts on planet one and they're going to be or orbiting this Center of mass in between them in the equation that represents that gravitational force is gravitational force is equivalent to the gra gravitational constant time mass of 1 * mass of 2 / our R 2 so R does not represent the radius although sometimes it can instead it's the distance between the centers um as seen here so something to note here and we'll get below when we derive for the uh orbital velocity is that centripetal force uh FG is the centripetal force for orbiting satellites right because when you're drawing your free body diagrams the only force acting towards the center for those satellites is the force of gravity because it is the shared Center of mass between that planet and that satellite all right so now let's talk about how do you calculate little G for Planet so we know that little G uh on Earth is netive or 9.8 m/s squar so how do you calculate that for other planets right so the equation for that is just the gravitational constant times the mass of that planet divided by its radius squared so here's an example for Mars we take the mass of Mars we multiply it by the gravitational constant on the top and then the radius of Mars we Square it and we find that the L G for Mars is 3.77 m/s squared so here is orbital velocity so orbital velocity represents that the speed that the object needs to go into a stable orbit all right so here we just start off with the centripetal force like we talked about before is going to be FG that gravitational force and so we can just replace FG with Newton's law of gravitation and then FC with the equation we had above here right mass time V ^2 R and so we can see the masses cancel on both sides and then we just multiply r on both sides to get rid of that r on the cental force side and we're left with v ^2 = G * Mass / R take the square root of both sides and we find the orbital velocity here's a very nice cheat sheet regarding Newton's law of gravitation uh we can see that the effect of masses on the left side and the effect of distance on the force of gravity so this is just a nice way to map out the different effects I won't go through it in detail you can take a screenshot if you would like but you can figure all of this out just by using the equation but just having these types of relationships um in your mind maybe even memorizing them at some point will definitely be useful and save you a lot of time on say like multiple choice questions that want you to compare the effect of increasing mass or increasing distance Etc and our final topic today is gravitational potential energy so what when we are on earth there is a constant gravitational field which is why we can use the equation gravitational potential energy equals MGH however when there's a non-constant gravitational field uh we're going to have to use this other equation which is gravitational potential energy is equivalent to negative gravitational constant uh time mass of 1 * Massa 2 and then divided by R distance between objects so it's very similar to new one's law of gravitation except the R is not squared and it is also negative so you're going to use this to find the gravitational potential energy between two objects or systems so that does it for the review uh for circular motion and gravitation hope you guys learned something and thank you for watching hey and welcome back to another video So today we're going to be going over the AP Physics one exam review for energy so yeah let's just get right into it so the first thing I want to touch upon is the types of energy so the first energy that we have is gravitational potential energy right so gravitational potential energy is going to be independent of motion and it's also based on the object's position in the gravitational field so what exactly does that mean well the important thing here is to identify the um what we call the horizontal zero line so if I have this guy on a cliff right and I use um MGH which is the equation for gravitational potential energy I can call that base of the cliff the ground y equals z so when I do my calculation MGH that height is just going to be the height of the cliff um but let's see I'm on an air plane right that height if I was to identify the horizontal zero line as the ground then that height would be thousands of feet right however if I identify the horizontal zero line um as y equal zero in respect to all motion um then that height is going to be much much lower and so my gravitational potential energy is going to be much lower as well so the next type of energy is kinetic energy so kinetic energy is just the energy of motion and you can see this through translational or linear kinetic energy or rotational kinetic energy and the final one is spring potential energy so that's just potential energy um that is stored in a spring and there are other ones like electrical energy but those aren't really relevant for calculations in this course all right so now let's talk about conservation of energy when there's no external forces acting upon objects in a system that is where energy is conserved so energy initial equals energy final all right so here's an equation that represents that and this is where there's non-conservative forces um that aren't acting upon it right so we're going to have something like air resistance or friction which is going to be represented as work other so kinetic initial plus u uh which is potential energy initial uh Plus work equals kinetic final plus potential energy final and uh something important to point out here is that it could just start off with all gravitational potential energy if it's say like ball released from a uh Cliff or something um from rest so that can always change but the point here is that energy can't be created and will always take other types of forms and that is where you have to represent them U using these equations all right so now let's talk about the concept of work so work is just change in energy it has a units of Jews or newton meters and it's equivalent to the force parallel times displacement and the displacement can both be either vertical or horizontal um so something to know about work is that work can both be positive or negative depending on the directions of the force in displacement so what I mean by parallel is that if the force is parallel to the displacement and they are in the same direction then it'll be positive work now if the force is parallel uh but in the opposite direction of that displacement then it's going to be negative work because it's going to be acting it all right and the graph of force time displacement is equivalent to work um and that can be easily seen through um that equation where the values are multiplied okay so now let's talk about work at an angle because when you have work um say you have a box or something and you you're pulling it um with a with a rope or a string or something that work is not going to be evenly distributed so that entire force is going to be acting on in component and that's a big part of physics where you have to observe things from a component perspective but now the equation changes slightly so now instead of work equals force parallel time displacement you're going to have work equals force time displacement time cosine Theta all right so here is a pretty nice chart which lays everything out so when that cosine Theta when Theta is in between 0 and 90° you're going to get positive value for cosine Theta and that also means you're going to have positive work which means the speed of the object is going to be increasing right because work is change in energy so if you're change in energy is increasing that means you have more kinetic energy um when Theta is 90° that means cosine Theta is zero which means you're going to have zero work and so the speed of the object is constant so when Theta is in between 90 and 180° you're going to get a negative value for cosine Theta and therefore you're going to get Negative work and so that means a decrease in the amount of energy which means a the decrease in speed as well now all right so the final thing we want to touch upon is springs and they'll get the power uh so for Springs there's two things you want to know and that is hooks law and the uh spring potential energy equation so hooks law um is states that the force on the spring is equivalent to the spring constant which is a constant force and it's just a measure of how strong the spring is times the change in length U from the equilibrium position so that is when it's not stretched um something to note here is that when it's osculating in simple harmonic motion or something um if it's the restoring Force it's going to be negative KX instead of just KX um because if you think about it um I should draw this out so if you have let's say this and then you have that spring here and there's a ball attached to the end so once it reaches its maximum displacement there needs to be a force which acts uh in the negative Direction here to get that uh ball to go back and osculate and go through its equilibrium position again so if we observe that chart or the graph of force over uh change in length from the equilibrium position that is going to be equivalent to uh K the spring constant which is the slope but like we talked about before the area of force over displacement is work and in this case we have force over displacement displacement from the equilibrium position and so we know that the area of this uh graph is also the change in energy right and so when you find this change in energy a lot of times what you'll do is then plug that in for spring potential energy so when you work with hooks law think Springs think spring potential energy um so that's something just to keep in mind so the final thing here is power so power is just how quickly does work happen and power is represented by the change in energy over change in time and that one equation will probably serve you well but there is another way of thinking about it so since change in energy we know on the reference table it's given as force times displacement right so if in our power equation we just we just substitute change in energy for um Force time displacement now we have power equals force * displacement over time now we know that D overt or displacement over time is just the velocity right that is just force time velocity right because D overt is the velocity and so power is also equivalent to force time velocity all right so that does it for today's uh review of energy for the AP Physics 1 exam if you guys learned something make sure to subscribe and if you have a question drop down below and thank you for watching hey everyone welcome back to another video So today we're going to be going over the momentum content for the AP Physics 1 exam um so momentum it is a vector it's denoted by the simple p and it's equivalent to mass time velocity and its units are kilog time m/ second so a mass motion will have momentum and you can think of momentum as how hard it is to stop something all right so the first big idea of momentum is conservation of momentum so in closed systems without external forces momentum is always conserved and we think about this again in terms of collisions so here's the general equation for conservation of momentum so it's just some of the momentum initial is equivalent to some of the momentum final very similar to um conservation of energy actually um so you can see here that if we have two objects let's say A and B and they're involved in a collision we can set it up where we break down each of the objects into their individual momentums so for momentum of a for example initial we can break it up into mass of a Time velocity of a initial uh Plus for B we have the momentum of b as mass of B time velocity of B initial and this gives us our corresponding final values as you can see there now sometimes uh momentum is not always conserved in both directions so you want to break up momentum into its components like we've seen in the other units right so because momentum just because momentum might be conserved in the extraction doesn't necessarily mean it's conserved in the y direction so that's just something to be careful of all right so here's a little bit about Center of mass so if there are no external forces the motion of the Cent mass will not change and this relates to the second point where the forces that interacting within the system will stay internal to the system so those forces inside the system are not going to affect the motion of center of mass or say the velocity of the center of mass um from its initial position so the second big idea is impulse so impulse is what changes the momentum of the object and it's denoted by the simple uh Newtons times seconds so impulse is a vector value and basically you can derive it from Newton's 2 law we can see here that acceleration can also be expressed as change in velocity over change in time um and therefore we can just multiply time on both sides to get ft equal m * change in v um so M * change in V is also just change in momentum um so change in momentum is equal to Ft which is equivalent to impulse and so here you can see on our motion graph here or rather just impulse graph it's Force time time um so you can see that the area under the curve represents the impulse which is change of momentum which is just final momentum minus initial momentum and now we want to talk about collisions so collisions are built on the foundation of Newton's third law so there's a mutual force that each block is going to be experiencing um when they Collide right so the first type of collision are elastic collisions so elastic collisions sort of Bounce in opposite directions and elastic collisions will conserve both kinetic energy and momentum so here's an example you have mass one coming towards uh sorry cart one uh coming towards cart 2 of M2 and cart one has a velocity of V1 uh cart 2 has a velocity of V2 and we can see that they're set equal to each other and so their total momentum um initially will be zero and so if we were to set up the uh total momentum equation of initial momentum equals final momentum this is what it might look like um we can see that we're just breaking it up M1 * V1 that represents the initial momentum of cart one and then everything final as you can see here Mass one vf1 uh etc etc now the second type of collision we have is in elastic so in elastic collisions where momentum is still conserved but now the kinetic energy is lost so let's say we have two masses coming towards each other we're going to have what is either perfectly inelastic so they're going to stick together and this results in the largest loss of kinetic energy and so we set up our our uh conservation of momentum equation we have M1 * V1 + M2 * vs2 is equivalent to M1 + plus M2 and then the entire thing times V and V is representing the final velocity which both blocks have because they're moving as one object as one unit in the system now they can also just be elastic so they're just going to generally travel in the same direction um and then the equation is pretty similar to the elastic equation except now taking into account those Vector directions um that is really what makes the difference um in these momentum equations so whenever you have a loss of kinetic energy and you're asked to calculate it all you have to do is use kinetic energy equal 1 12 MV squ um you can see has the variables of mass and velocity which usually you will be able to uh solve if you're doing momentum equations um so you use this to find the loss of energy and now just some final things quick tips for momentum problems make sure you draw your diagrams and list the Givens always for any type of problem identify whether there's impulse or conservation of momentum it'll help you get started with problem solving and then you also want to account for velocity vectors and directions that's super important um especially for collisions I mean it can absolutely make the difference so yeah that does it for this quick content review for momentum if you guys learned something make sure you subscribe and thank you for watching everyone so today we're going to be reviewing the simple harmonic motion content for the AP Physics one exam so simple harmonic motion doesn't account for for a big percentage of uh the national exam but it's still a nice refresher in terms of pretty much every unit right like forces energy um and a bunch of stuff so simple motion so what exactly is it so it's whenever you have what is a repetitive motion and it's going to occur because of a restoring Force which is always trying to push the system back to its equilibrium position so in these examples you'll see conservation of energy uh negligible and stuff like that so A couple key vocab terms that you're going to need to know for this unit is period so that's a time it takes to complete one full cycle um and pretty much return back to its starting position after it osculates then you have frequency that that's sort of like the inverse of that that's just the number of cycles per second so you can see the equation of tal 1 over frequency um and then you have amplitude right that's just the maximum position from the equilibrium position that your block or your pend reaches um when it osculates so let's first look at a pendulum so the equation for a pendulum is 2 pi * < TK of length of the pendulum over the gravitational constant so something to know about the equation is that it is independent of the amplitude right so if you zoom in on this ball we can see that what is the restoring force is the tangental component of FG and this is the uh Force right here um you can see that that mg sin Theta is what gives you that tangental force and that's going to push that pendulum back towards this equilibrium position it's not going to stop there um because there's conservation of energy right so it's going to go from its maximum amplitude position to its maximum negative amplitude position and as you increase that angle of uh release the initial release position that's also going to affect the mg sin Theta for the tangental component of FG and therefore your restoring force is also going to change next let's talk about the horizontal Mass spring system so this is frictional so the equation for a spring is just 2 pi * Square < TK of mass over the spring constant it is also independent of the amplitude so here's a nice diagram it shows that initially your block is at rest and what is called equilibrium all right but let's say we stretch it out so now it has spring potential energy um so at this position the acceleration is going to be negative Max um the force is going to be maximum and your velocity is going to be zero so this isn't really representative of you pulling it and stretching it to that position but this is just when it's oscillating when it reaches that position these are the uh standard values so if it goes from position 2 to three when it's osculating when it reaches the equilibrium position your force on it is going to be zero and therefore your acceleration is also zero and that's also when you reach your maximum velocity uh when it reaches the other side the other side that negative amplitude it's very similar to position two where the force is maximum but the acceleration is also maximum except now it's in the positive direction because you're trying to go to the right side right to bring that uh Mass on the spring back towards that equilibrium position and then your velocity is zero all right so here is a table summary of just general simpler amount motions and on this side we have some motion graphs so these motion graphs are just a way to represent motion and we can see that it's representative of this spring Mass system that is oscillating so if we look at it position two represents that maximum position away um as you see here position two maximum distance uh away from that equilibrium position and therefore at the maximum amplitude in the positive direction and then as it goes toward is that equilibrium position you're going to hit xal 0 which is representative of position three then it goes to its negative at 4 and comes back now for velocity you see a very similar Trend so for the maximum position at two you can have zero velocity right because acceleration is Max the force is Max but when it reaches the end points of equilibrium position so position 3 that is when we talked about how the uh velocity is going to be maximum right so you see how the velocity for uh position three is maximum whereas the other positions the velocity is zero now for acceleration very similar Trend so when it reaches its equilibrium position there is no acceleration but when it reaches its end points it has that maximum acceleration so that's just a quick content review of simple arotic motion if you guys learned something make sure you subscribe and thank you for watching hey everyone so today we're be going over the AP Physics 1 torque and rotational motion review for the AP exam um but this is also a great content review for just your in-class exams so let's get right into it so the first topic here is angular kinematics so the thing with this unit is it is kind of a summary of everything you've learned so far this year right so the first unit is kinematics and now we have angular kinematics so it's sort of a spin-off of that um so just a couple key terms here angular position which um we can represent as the displacement is just change in the angle there is angular velocity which is represented by this W looking symbol and then there's angular acceleration which is this fish looking symbol um so here's a nice diagram of a circle representing um this angular kinematic uh breakdown so the positive direction is is defined as counterclockwise and the negative is defined as clockwise and you can see that as the object rotates that causes a change in that angular uh position and that angular position is equivalent to one revolution is equivalent to 360° is equivalent to 2 pi radians so you really want to drill in and know those convergence because a lot of questions are going to give you something and let's say radians and then they want an answer and say like Revolution so definitely know how to convert between those units another thing to know is that there is the same angular velocity and acceleration uh for all points of the same rotation all right um another thing is that points that are closer to the center have a decreased linear velocity and we'll talk about that down here so there's less distance in one revolution that is because linear velocity um corresponds to the change in distance right if you think about it if you have a larger radius it's going to result in a greater change in distance when the rotation rate is the same so let's say you had two circles right one Circle was 2 cm in diameter another one was 10 m in diameter but they both rotate around in 2 seconds they complete one revolution in 2 seconds the one with the 10 m radius is going to have a much greater linear velocity here's another very important key concept the connection between um linear motion and angular motion right so for linear you have your X which is equivalent to the angular angle the linear velocity and the angular velocity linear acceleration and angular acceleration and you can easily convert between both linear and angular values by just using the radius so the radius sort of connects both the linear and angular components so this is just a side note regarding forces um when you have something that has the same rotation rate and you're trying to compare it you can uh observe it using circular motion right so net force equals ma the acceleration is going to be equal to the centripetal force so we can just call that v² of R and then just replace v^2 with um angular velocity times R 2 because as we said before you can connect linear and angular motion and that gives you the net force exerted when you're observing it from an angular perspective all right so motion graphs so this is very similar to just linear kinematics um you can see some examples of position over time angular velocity over time and angular acceleration over time um so the slope of each one corresponds to uh each other so the slope of position over time is these uh angular velocity and then the slope of the angular velocity over time is the angular acceleration and then as for the areas the slope of the angular acceleration over time is the change that's very important is the change in uh angular velocity and then the area of the angular velocity over time is the change in angular position and here are the universally accelerated motion equations that you'll be using so this is pretty much identical to the linear equations they use for kinematics and so you want to use these when angular acceleration is constant you can see all the variables are pretty much just swapped with their linear counterpart all right so the next big topic is rotational torque so this sort of connects with forces and Dynamics right so a net torque is going to cause angular acceleration and the equation here is net torque equals moment of inertia which is sort of like Mass except it counts for how mass is distributed uh times angular acceleration so that's very similar to net force equals ma all right so a greater moment of inertia will lead to less angular acceleration given the torque is the same and vice versa for Less moment of inertia and here's a very nice diagram that sort of shows you how moment of inertia changes based on the concentration of masses and here's another diagram depicting a really nice example and we'll get to it more when we talk about rotational energy um but this is where we're talking about what is causing that net torque and because of the way the equation is set up uh if I can find it right here torque is equivalent to force * R sin Theta so if you apply that there's a 2016 F frq on this I did a video on it um where I found that the force of friction is the one that actually causes the torque so if you're wondering why um definitely go check out that frq video um FG and FN do not cause a net torque here to do that equation and so you want to draw all the forces from the position in which they act um especially for free body diagrams all right so now let just talk about the general torque and how it works so torque is not a force essentially but it's sort of is the thing that causes objects to rotate around a Axis or pivot so it's sort of like a collection of all forces and then is just a a way to represent them so torque is equivalent to force which is just the force exerted times R which is the distance from the pivot that the force is applied that can also be interpreted as radius and then in some examples you can use sin Theta and Theta is measured in respect to the radial line and here's a wrench and it's showing you um how the only component of of the force as perpendicular to the radial line which is R uh is the one that causes the torque so you can observe it in two ways here if you use this pink angle you'd have to use cosine to find that perpendicular component if you use this uh green side over here you use the sin Theta all righty so torqu in equilibrium so here is a example of that where we can see we have a guy standing on one side of this plank thing but the plank thing since it is off its Center of mass um all of its mass acts at the center of mass so it's not depicted nicely here um but there is a 100 Newton torque that acts clockwise um in this problem we can see here and so the torque that the person is exerting is going to be in the other direction counterclockwise and that's going to be the force of gravity and so here is the equation that shows you how it's being represented in this example all right so now let's talk about rotational energy so for rotational energy it is equivalent to um when you talk about kinetic rotational energy we tal it's equivalent to 12 * moment of inertia time angular velocity squar so that's pretty similar to translational or linear kinetic energy um which is 12 mv^ 2 um you can see how there's correspondence between moment of inertia and mass and then angular velocity and linear velocity so here we have a a ball object thing that is rolling down so the force of friction like we talked before is going to be causing that uh angular acceleration and since it points clockwise that angular acceleration will be clockwise as well and since a linear velocities is already pointing in the clockwise direction it'll be speeding up and getting faster and so it starts with gravitational potential energy assuming it's uh released from rest and that's going to be converted to both kinetic translational energy uh as well as kinetic rotational energy now it's a different story when the ball is rotating up because now the force of friction is pointing upwards um and so it's going to be causing a angular acceleration CL counterclockwise and because the ball is rotating upwards right there's that initial angular velocity going up but that is pointing clockwise whereas the force of friction causes that angular acceleration to be counterclockwise and so angular velocity and linear velocity will be decreasing and then for energy it would be kinetic energy translational plus kinetic energy rotational to start and that's all converted to ug assuming the ball stops somewhere at the top all right so the final topic is angular momentum so angular momentum similar to linear momentum is a vector the symbol for it is L um and these are the units kg * mass s over seconds so if there is no external torque angular momentum changes you can see the equation for that where uh torque exerted over time is equivalent to the change in angular uh momentum so if there's no torque um there's no change in angular momentum so England momentum would be conserved now regarding collisions so linear momentum we talked about collisions there so that still applies to England momentum and so if there are no external forces on a system in elastic collisions then the total momentum is conserved and kinetic energy is conserved as well and then for in elastic collisions only momentum is conserved and kinetic energy is lost and for perfectly inelastic collisions it's going to stick together and that is the greatest loss in kinetic energy which you can calculate and just some final equations to note down here is the angular momentum of a point mass is just MV note that is change in linear momentum times radius and then we have our standard uh angular momentum equation which is equivalent to moment of inertia times angular velocity and the same principles of conservation of energy conservation of momentum um conservation of now angular momentum you can see that if there is no net torque then it would balce out just like how we talked about MV equals MV now we have moment of inertia times uh angular velocity is equivalent to the final moment of inertia times final angular velocity all righty so that does it for this review hopefully you guys learn something if you have a question drop it down below and thank you for watching