so this is a summary of the mechanics part of the edexcel international a level and the first thing i want to look at are motion graphs so for this first graph over here what we're going to have is our displacement which we're using the letter s for and we've got time along the bottom now often we measure our displacement in meters and our time in seconds but sometimes we do have maybe hours or even kilometers on some of the graphs that you might see so what we can do is actually look at the motion of objects and look at how their displacement changes with time and because displacement is a vector quantity we can have both negative and positive values now in this graph over here we've got the region where we have a straight line which is flat and that's where something is stationary so it's not moving and then we also have a region where that displacement is increasing and actually what we find is that the gradient or slope of the line is equal to the change in displacement with respect to time and this is what we then call the velocity so the gradient here represents the velocity and if we have a negative gradient that means something has a negative velocity but we can also look at velocity time graphs with velocity measured in meters per second and time once again measured in seconds and if we had a graph like this where we have this constant gradient this gradient now represents the change in velocity with respect to time and this is what we call the acceleration so the acceleration is going to be equal to the gradient because that's going to be the change in velocity with respect to the change in time now over here we have a constant gradient and therefore we have a constant acceleration but sometimes we get a graph with a curve and this means that at different times the acceleration is going to be changing if you want to find out the acceleration at any particular point what we then do is we draw a tangent to the line maybe we're going to look at this point over here what we would do is draw a tangent and then you could then work out the gradient of this line to work at the instantaneous acceleration at that point now the other thing about a velocity time graph is that the area between the line and the axis actually means something and the area of this graph over here which i'm just going to shade in like this this is equal to the displacement of the object now the two ways to work it out sometimes if you have a shape with maybe some straight lines you can work out the area by calculation sometimes that's a little bit tricky especially if you have a curved line and what you can then do is you can count the squares now sometimes calculation is going to give you the best answer but sometimes you might do it by counting squares which is a good way of estimating the distance traveled in a certain direction that displacement now the other type of graph which comes up not as often is an acceleration time graph and this graph might show how the acceleration that isn't constant changes with respect to time perhaps you've got a falling object which as it increases its velocity the drag increases and therefore the rate of acceleration decreases so displacement velocity and acceleration time graphs these are really important because they visualize the motion of an object but these also introduce some equations and what we can also think about are the equations of motion these are sometimes known as the suvat equations and a lot of you might have seen these in mathematics as well and what these look at are when we have a constant acceleration and we maybe know the displacement the initial and final velocities and also the time taken and there are four main equations that we use all the time and these are brilliant at looking for this uniform acceleration in one dimension now what i'd recommend doing is writing suvat vertically down when it comes to any questions you can then identify any quantities which are named within the question and also identify the thing that you're trying to find what you'll also notice is that this one over here doesn't have an acceleration term in it this one doesn't have displacement this doesn't have the final velocity and this doesn't have the time so provided you know three of these quantities you can then work out the fourth and once you know four you can work out the fifth so these equations are so useful and you're going to see loads and loads of examples throughout the whole of a level physics and these equations are looking at vector quantities and it's just worth reminding ourselves about the difference between vectors and scalars so both of these are quantities and that means they have a size or what we call a magnitude so a vector has a magnitude and so does a scalar but a vector the direction is important as well so examples of scalars include things like distance and speed whereas when you come to vector quantities we're thinking more about displacement which is just the distance traveled or moved in a certain direction we might think about the velocity which is then the rate of change of displacement we have things like acceleration and so on and when it comes to representing vectors in physics what we need to do is use arrows to represent these where the direction of the arrow represents direction and then the size or the length of the arrow represents the magnitude you're going to come on to doing lots and lots of vector diagrams and this is also important because what we can do is we can add vectors together and also we can resolve them into their horizontal and vertical components both doing it by scale drawing and also by calculation so first of all let's imagine we have a vector which is v at an angle of theta to the horizontal direction over here what we can actually do is think about this vector we can think about how much of that vector is maybe acting to the right and how much of that is acting upwards and we could maybe call this either the x and the y direction sometimes we call it the horizontal and vertical so what we can do is we can split this into its component parts so i've called this one in this case v x and i've got v y and this is where trigonometry is important and it's useful to recognize maybe the angle the hypotenuse the adjacent and the opposite let me just draw that on a triangle over here to just show how this is so important and it comes up all the time in a level so this is my right angle triangle and i've got the angle theta and the side opposite to this is the opposite side the longest side is hypotenuse and then the side next to the angle theta is the adjacent side and it's always just worth remembering sokatoa and this then lets you know the relationship between two sides so what we can say is that sine theta is equal to the opposite over the hypotenuse cos is the adjacent over hypotenuse and tan is opposite over adjacent now this is really useful because this allows us to work out what v x is in terms of v and theta so what we have here v is like the hypotenuse the v x is like the adjacent and if we've got the adjacent and hypotenuse we're going to use cos so we can also then say that vx is equal to v cos theta for the horizontal component of this vector and the vertical component is going to be similar to the opposite side so we're going to use sine so we can say that v y is equal to v sine theta now when you get to some more complicated problems it's often you know is it sine or cos which do you choose it's just worth drawing out a triangle labeling which is a hypotenuse the opposite of the adjacent and that allows you to choose either sine or cos don't forget of course that we can also resolve vectors not just vertically and horizontally but also in the direction of the slope that maybe an object is sat on so perhaps you have an object which is sat on a slope there's maybe a weight force acting down we can still resolve this weight into its components but rather than doing it vertically and horizontally we can do it in the direction of the slope and also normal to the slope and again this is why it's important to think about the relationship between sine cos and the different size of this triangle now the other thing we can do with these vectors is we can actually add them together now if you're going to be doing scale drawing you need to have a long ruler you need to have a protractor and a pencil and you need to take care when you're actually drawing these so say for example we had maybe a vector which is drawn at a certain angle to the horizontal we can add the vectors end to end and this is where depending on the data you've been given you have to very accurately or as precisely as you can measure out the angles and what we can then do is we draw in maybe two vectors that we're adding together and this is where they aren't at 90 degrees together so there might be an angle which is greater than 90 degrees and to work out the resultant what we just need to do is simply draw a line from the very start to the very end and the length of this line is going to be proportional to the size of that vector you might choose something where maybe one centimeter represents one newton but really this depends upon the data that you've been given in your question and how much space you have available now because it's a vector we don't just need the size or the magnitude we must also measure the angle and then label where the angle is from sometimes it might be a bearing from north sometimes it might be an angle from the horizontal so scale drawing is a really useful way of adding vectors especially when they're not at 90 degrees to one another the other way that we can do it and this is what i think students tend to prefer is we might do it with calculations so perhaps we had two vectors which were at 90 degrees so maybe vector one and vector two and their resultant is going to be in this direction over here it's gonna be up and to the right in this case now we can think about this if uh if i just draw in a parallel line to this one over here of the same length like that then the resultant of this is going to be from this position here to this position over here now to work out the magnitude of that what we can use is pythagoras because we know that this side squared is equal to this side squared plus this side squared and this side is the same as vector 1 over here so v1 squared plus v2 squared square rooted gives us the magnitude to work at the direction maybe we've got theta in here again we can recognize that we have a right angled triangle this side is like the hypotenuse this is the opposite and that's the adjacent and to work out the size of theta theta is going to be related to the opposite and the adjacent two values that we've been given and it's going to be inverse tan of that so we can do adding vectors either mathematically which gives us a really nice precise accurate answer or we can do it by scale drawing which is often sometimes faster and quicker but again you will be directed towards either this method or that method when it comes to any questions now we've seen that we have these see suvat equations of motion and these can also be used for looking at projectiles and this is where we have both horizontal and vertical motion now the two main types we get are when something is maybe projected up and then down like this or sometimes we maybe have something which is leaving something horizontally and it falls down and these are both great examples that show the independence of vertical and horizontal motion now we're going to assume that we have ideal conditions where we've got maybe a mass which is only accelerated by gravity and that means that air resistance is going to be negligible and that means we can ignore it when we look at our calculations so the horizontal velocity is going to remain constant so let's imagine we had an object at the start maybe at its midpoint and at the end the horizontal component of velocity which i'm just doing here is going to remain exactly the same size throughout its whole motion and if we think about maybe an object over here which is maybe just coming down once again the horizontal component of velocity is going to remain the same throughout what is going to change though is that vertical component of velocity because there's always going to be an acceleration downwards so maybe if we've got something which is projected up and then down initially it has a vertical component of velocity upwards at the top it has no component of vertical velocity and at the bottom its vertical component of velocity is going to be down and if we've got something which is maybe projected horizontally and then it falls under gravity there's going to be no vertical competitive velocity here it's going to be small here and then it's going to be largest at the very bottom now my top tip is once again write out sue that and you can maybe think about sue that in the vertical direction and you could also think about suvat in the horizontal direction now the thing is in the horizontal direction because there's no air resistance the acceleration is going to be zero and that means it's going to have the same velocity u and v throughout so these two things are going to be the same size but what you can then do is you can start to identify from the questions things that you do know and often you find that actually the time is going to be the same so if you know the time horizontally that's going to be the same time as vertically and the other thing to make sure is that you label which way is positive you might say that downwards is positive or you might say that upwards is positive if you've got maybe something like this you might take upwards as a positive direction and that means you'd have a negative acceleration of 9.81 meters per second squared throughout so projectile motion this is the ultimate test of you knowing your equations of motion now so far we have loads of equations that describe what happens when we have bodies which are accelerating but what causes that in the first place and this is where we need to think about maybe the forces which are actually acting on something and what we can do are what we call free body diagrams and these are just really simple ways to represent the forces at you on something so we might think about maybe the force down due to weight there might be an upwards force due to the normal contact force and there might then be a force which is maybe acting to the right now once we have this object which has various forces labeled we can actually think about what is the resultant or net force of that and what we can say is if we sum up the forces actually on this object which has a mass that's going to be causing this mass to accelerate so this here just represents the resultant or net force now this equation is a special case of newton's second law and provided we have a constant mass and we have a uniform acceleration we can say that the resultant force is equal to mass times acceleration now there's also a case where we have newton's first law and again this is about the forces acting on one object where newton's first law what we have is something where there's no resultant force because the forces on that body are balanced and if there's going to be no resultant force that means there's going to be no acceleration and that means the object will either remain stationary or will continue moving at the same velocity and this is something where we maybe have an object which is falling and if it's falling there's going to be a force down due to its weight but if it's moving at a certain velocity the drag force ends up being equal in size to the weight but in the opposite direction and that means here the sum of the forces is zero that means there's no acceleration but this object keeps moving so what we have now is something moving at terminal velocity and because the resultant force is zero the acceleration is zero and that means the velocity is constant and it can be things which are falling but it could also be things which are rising up at a constant velocity or even things moving horizontally so terminal velocity is just one example where we have newton's first law in action but newton's second law applies to so many other things but why do we have this weight in the first place well if we think about forces we also often use little g and this represents the gravitational field strength and the gravitational field strength is the force per unit mass and that means we give it the units of newtons per kilogram and this is equal to 9.81 newtons per kilogram and this is on earth again this is going to vary depending on the mass of the planet and it's something you're going to investigate a lot more when you look at gravitational fields next year now if you have a mass inside a gravitational field it's going to experience a force which we call weight and we can calculate the weight that that object experiences by multiplying its mass by the gravitational field strength not forgetting of course that mass is measured in kilograms but weight is a force and therefore it's measured in newtons now so far we've looked at the forces which act on one object so newton's first law and newton's second law are both concerned with one object and the forces it experiences but we also have newton's third law and this is about the forces experienced by two different objects i'm going to call them object a and object b so newton's third law is looking at the forces between two different objects we can say that the force of object a on object b is equal to an opposite to the force of object b on object a now these are the same type of force they're the same size and they act between them whereas when we think about newton's first and second law we're just considering the forces acting on only one of those objects now we can also do an investigation into the acceleration due to the gravitational field strength on earth and we can do that to measure the acceleration due to gravity and in this core practical what you might have is maybe a steel ball bearing and actually what we can do is we can let this fall through a certain distance which i'm just going to call h to be the height and what we can then do is record the time that it takes to fall through this distance now you might have some kind of data logger and this can maybe turn on when an electromagnet holding this ball bearing up is turned off and then you might have a trap draw at the bottom which opens and that turns off the timer now if we're doing this we have a certain height that's measured we record the time and we can effectively think about writing down sue that to find out what we do and don't know now the displacement vertically is its height we know that its initial velocity was zero the acceleration is due to the acceleration due to gravity and then we record the time and if we know s u a and t we can use the equation that says s is equal to u t plus a half a t squared and because u is zero s is the height the acceleration is g and therefore h is equal to a half g t squared or we can also say that the acceleration due to gravity is equal to 2h divided by t squared now the setup when you actually do this in school might vary but effectively if we've got measurements of height and we've got values of t squared we can use this to find our value of g because what you can do is you can alter the height it drops through you can record the time and if you were to plot a graph where we had 2h on the y-axis and we had t squared on the x-axis what we should get is a straight line that goes through the origin and here the gradient of that line is going to be equal to the acceleration due to gravity which should be in the order of 9.81 so that's a core practical that at some point you should see demonstrated or have a go at yourself in school now another thing we're going to be looking at is something called momentum now momentum is a property of moving objects and here we're talking about linear momentum so this is objects which are moving in a line and we can say that momentum which has a symbol lowercase p is equal to the mass of the object multiplied by its velocity and because we've got a vector quantity here for velocity the momentum is also a vector quantity and therefore it can have both a positive and a negative value and the units for momentum are kilogram meter per second now the important thing about momentum is it's a conserved quantity and if you had a collision between two objects or maybe you had an explosion where two objects move away from each other we can say that the momentum is conserved and that means that the momentum before the collision which i'm just going to call p before is equal to the total momentum after the collision and this is for a closed system where there's no external forces being applied and this is really useful because it allows you to maybe work out maybe we had two objects which maybe were moving towards each other beforehand we could work out what might happen after this and maybe the two objects bounce apart or maybe they stick together and they move off together again the question is going to direct you towards what actually happens and if we know the mass of this object and the mass of that object how quickly they're moving we could then maybe work out the final velocity of this system afterwards and this is because we can work out the momentum of this object in this object beforehand and that's going to be the same as the momentum of these two objects afterwards now another way of writing newton's second law isn't just to say that the sum of forces is equal to the mass times acceleration we can also say that the force is proportional to the rate of change of momentum of an object so looking at delta p over delta t which just means a change in momentum with respect to time and this is a better way of actually talking about newton's second law what we're saying is that force is proportional to the rate of change of momentum and it's only if you have a constant mass and a uniform acceleration can we actually write f equals m a so now we know a bit more about momentum this is our better definition for newton's second law but effectively if there's no force there's going to be no change in momentum and that means then the acceleration would be zero now something which sounds similar to momentum is moments so let's have a look at some moments now to calculate the size of the moment that's equal to the size of the force multiplied by the perpendicular distance between the pivot point or the point that we're taking the moment about and a line of action of that force so effectively this distance here is at 90 degrees to the direction of that force and because we measure force in newtons and distance in meters the units for moments are newton meters now another topic linked to moments is the center of gravity and the center of gravity is effectively the point at which the weight of an object appears to act so maybe we have this shape over here the center of gravity might be at this point over here now if this was maybe hung from a point over here so maybe this was suspended from a point what we'd find is that the weight of the object was acting down in this direction so that's a force but this is acting at a perpendicular distance away from the pivot so that distance x you can just about see in here is going to cause there to be a resultant moment on this thing and if we think about this this resultant moment is going to have a turning effect and that's going to cause rotation in this case going anti-clockwise so there's going to be an anti-clockwise moment and that's going to happen until the weight is directly beneath the pivot point because then the distance x is going to be zero so this is why if you have a shape and it's suspended freely from a pivot point the center of gravity is always going to be directly beneath that pivot and this is because the object is now in equilibrium and that means not only are there forces on it balanced but also the resultant moment is going to be zero because the anti-clockwise moment is equal to the clockwise moment and that's what happens when we have objects which are balanced so we've looked at equations of motion we've looked at a load of work about forces and the final thing to consider is work and energy now we might think about the energy that's stored by a moving object and we call this its kinetic energy and that's equal to a half times its mass times its velocity squared so this is the energy stored by something which is moving but we can also store energy in the gravitational field and what we can say is that the change in gravitational potential energy is equal to its mass times the gravitational field strength times the change in height and this is where we have something where the value of g is a constant so maybe near the surface of an object like the earth and effectively as you change the height you move something higher up it's going to store more energy in the gravitational potential store now how can we actually maybe increase the kinetic energy or the gravitational potential energy well what we can do is we can do work on an object and work done is equal to the force multiplied by the distance moved in the direction of that force so what we're looking at is a change in displacement and this tells us the change in the work done on that object now not forgetting of course if we have a force acting at an angle to the direction it's moved it's only the component of force in the direction it's moved that we're going to use in this equation so sometimes we might need to use cos theta for this so work done is the amount of energy transferred to an object and here we have kinetic energy and the gravitational potential energy all of these are measured in joules and it's really worth just saying that just like momentum energy is a conserved quantity so energy cannot be created or destroyed it's just transferred from one store to another and actually that's really useful for calculations if we maybe knew the gravitational energy that something had at the beginning that might all be transferred to the kinetic energy at the end and if we can work this out we can then maybe find another quantity now the other thing which is really important isn't just how much energy is transferred but the rate at which it's transferred which is what we call the power so the power this is a capital p for power is either the energy transferred per unit time or it's often worked out as the work done per unit time again both of these are measured in joules this is in seconds and the units for power are watts now most of the time we don't get something where 100 of the energy goes exactly where we want it to and it's important to consider the efficiency of a system and efficiency is just the ratio of the useful energy output divided by the total energy input we can either give it as a number between zero and one or we can give it as a percentage between zero percent and a hundred percent now again any energy which doesn't go usefully where we want it to go it's not been destroyed it's just been maybe dissipated to the surroundings or it ends up in a unuseful energy store now we can do it with the useful energy output over the energy input but because power is just the rate of energy transfer we can also look at the useful power output divided by the total power input so this was just a summary of the mechanics topic it has things about equations of motion about forces about energy you're going to build upon this knowledge as you go through the course and you're going to continue to really understand this as you apply your new knowledge to many more questions thanks for watching and i hope this has been helpful thank you you