in the previous video we looked at the basic terms of how to upgrade our understanding of kinematics but now with angular angular thing turning in a circle so today when we look at how to understand what is centripetal acceleration and force and where is it okay go back to this circle first question for you to think about look at this diagram we have velocity right i'm going to change them a bit so that we have the final velocity v f which is b okay this is the final velocity vb and we also have initial velocity which is when the particle is starting off at a so this is va okay so how where is acceleration ah that's my question for you how to find acceleration where will we draw the arrow once upon a time if i say oh i drop a ball the ball is falling down okay so it has a velocity downwards faster and faster so maybe at first initial very small then downwards very big while because of acceleration pointing downwards we know where to draw the acceleration actuation down up left right now in a circle where is acceleration uh are you how do you think about this thing okay so we're going to look at some observations of how the thing moves in the circle to figure out actually where acceleration pointing are is there even acceleration miss acceleration is change in velocity over change in time is there a change in velocity let's look at the let's look at the table on the right so the first observation we have here the direction of velocity vector of the particle is tangent to the circular path tangent means you just touch it at a certain way where this purple color let's see va is right angle to the radius that's how we know it's tangential this right angle so that observation tells us something already your path is curved but your velocity is a straight line so one moment now your velocity is like this another moment certainly a point another direction already direction is changing there so that's the first observation we can note an inference for so if your if your velocity vector keep changing ah you can say it means that the direction of velocity remember that velocity is vector your point here point that is different one okay the direction of velocity changes all the time yep all the time as long as you are turning your arrow is changing so i don't know the point where you are going okay second observation let's go back to the circle so velocity we mentioned is a vector can we write down first velocity is a vector so when the direction change velocity change although let's say the purple on the left side you say is 5 meter per second let's say after that you go to the other side already it is still 5 meter per second okay that one speed is constant 5 meter is still 5 meter but the direction is now different so velocity has changed so we can conclude here that if there is a velocity change change in velocity which is a vector then you can see the particle is accelerating how we know that because i uh got change in velocity means got acceleration low likely so okay one moment you point here one moment your point here although the v is still the same but the velocity vector is changing okay so last thing then so we are sure that it's gonna be acceleration so where is it going to be directional acceleration actually is directed to the center of the circle center of circle or sometimes we say the direction is center of circular path okay and it is also known as sentry pito acceleration special car acceleration a but with a c there okay center of circle or circular path no space now circular path bit small all right okay so how do we how do we convince ourselves that this we're gonna do some vector drawings right here play with the arrows a bit so if i want to find my centripetal acceleration or just say the vector what do i need to do i need to take my final velocity minus initial velocity divided by time but that's vectors so v b which i want to give it a vector hat minus v a is going to be my acceleration how do we do vectors again let's copy paste is my attempt to duplicate vb okay that might allow we just vb okay then va but don't forget this is minus va so we need to minus va means the va become backwards or so minus remember your vectors from a s okay we need to flip the vectors backwards so i'm going to join this tip to tail oh it kind of joins up like that i'm going to label this v a but we minus v so this is negative v a so the vector is pointing the other way which means our acceleration will be these two together so acceleration will be the third arrow which is this resultant force sorry don't result in phosphorus resultant vector acceleration okay so that's how our assertion would look like we can move it around so this one is taking an average between these two intervals vbva so somewhere in the middle or something like this okay i will redraw it right here so acceleration if we were to draw the vector is pointing like that towards the center of the circle over that change in velocity vb minus v8 okay so now that we know where it's going to be pointing can we write down here at the right point the center of circle okay this time very important you must know where is it so you're constantly accelerating towards the center you're you're poor particle actually you want to move in the straight line one particle say ayah means i want to go in a straight line but then nope you have to move in a circle why are we moving the circle something else is causing it to accelerate to the center so you always accelerate the center okay then you want to move here already somebody pull you down okay now you are here you want to move down away from the center but somebody pull you down so you are perpetually going towards the center and that can only happen acceleration is related to who force god force got acceleration so we say oh hang on a second newton's second law says a net force is related to acceleration if you've got acceleration happening there must be a force and there's a special name for it we call this and we say that a resultant force because acceleration a resultant force is necessary hey i didn't write fosa okay i put f a resultant f is necessary for any object for an object to change direction or to travel in a circular path or circular motion okay to provide what we call a special name to provide centripetal force ooh what is this centripetal force okay pause it a bit object if you don't exert force will stay at rest okay remember newton's law if this fellow is chilling here it's just going to chill there if you are in bed you are in bed if you are already moving in a straight line without any resistance no friction nothing then you just continue moving in the straight line forever but now you keep changing direction so there's a force force first false force but what is a centripetal force hmm let's look at some pictures so here are some examples of other kinds of circular motion look at the first one this lady is swinging a ball around why the ball can move in the circle i thought ball would you throw it go in the straight line one yes what is the force here that is pulling the ball in a circle look carefully at the picture the string you see this string there's a tension force t for tension so tension provides a centripetal force which is a resultant what is pointing to the center tension now so you say tangent if you look on the right a car turning around a bend the car supposed to go in a straight line why certainly can go in a circle think carefully oh the tire means the tyre will help you you turn the wheel the tire will turn my right but you see if you are on ice you drive on a smooth surface and you try to turn cannot your car will go and crash into the some mountain straight away feel fly there and crash it's because your tire got grip got friction ah so what is this red arrow this arrow is really frictional force of your between your tire and your road and this is known as the centripetal force so here we will say friction provides who provides centripetal force to allow this thing to go in the curve friction provides centripetal force next come see you can see more interesting things well this roller coaster also can can anything got curved a bit essential circular motion already why this roller coaster can turn out a bit more challenging already so you see the curve white is pulling it down weight gravity oh but it's also two fours there got one here got one here we will learn more about this in the coming section but i'm going to put here what is this anna normal contact force the the purple color track push up the car right so that's normal force and and what is this one mg weight of the roller coaster n and mg both of them provide centripetal force means why got two one because both are within the same line of radius away from circle away from circle here away from circle and this is how the circle look like so you see now what is the force pointing to the center or away from it that contributes to centripetal force last one pretty easy one you see there's a earth going around the sun means why the earth go around the sun why don't the earth just go away oh trust me the earth wants to go away a certain velocity just fly away why cannot somebody pull it ma gravitational force so here you see this one this pink color arrow this is our gravitational force the sun pull the earth and that contributes to what we call the centripetal force so who provide centripetal force we say here gravitational force f g we'll learn more about this in the next chapter after this so there's two equations or two main bunch of equations you need to know for force and acceleration go acceleration means got force force missile acceleration they're related so the very first one centripetal acceleration write this down if you have not we need to know that there is a centripetal acceleration we use a sometimes we put the c down there sometimes we don't put the c so just if we circular motion you got a you assume is centripetal acceleration okay so centripetal acceleration is the equation for it that's v squared over r if you are curious to know means where this v square over r come from go check out the bonus video which derives this equation if you want to know about it there's some maths involved just a heads up okay so one form is right as v squared over r another form is to substitute in a equation for v so previously we look at v is what tangential velocity right you see here v equals to r omega we can plug that in here what do we get so since we have let's put the v here v equals to r omega we can sub that in and we will get r omega square that's another form of this equation so you can either use this or this but make sure you know how to to remember or recall these equations in the first place the second one we need to know is centripetal force on the right side so what are the equations for centripetal force if you don't know where to start you go newton's second law okay miss f net equals to m a but now we are looking at the centripetal thing so if you want to you can add fc and the ac everything is thrown inside there so in substitute centripetal force fc whoever contributes to it i'm i'm gonna drop the the sum of m v squared over r where the v squared over i come from here on the left side i plug in this v square over r inside this acceleration so let's draw a little bubble equals to v square over r that's how i sub in that value so this is the very first equation to use in this whole chapter another form is oh we can sum in r omega square also right okay you also can use v equals to r omega sub in then what do we get we get fc equals to m r omega square okay so to summarize here's one common explain explain explain question which may appear and kind of also it was a good point to summarize everything here okay so how do you think of circular motion why can things move in a circle because somebody is pulling it i pull you around me and then you will go in a circle around me okay so why circle in the first place firstly whenever you do this kind of question you must identify who provides centripetal force is it gravity is it a string is it normal contact forces are some of the possible choices so gravity and what else are tension string normal contact force what who who is the false pulling so there will be some kind of force let's say let's label this pointing towards the center of a circle okay and this is some force which contributes to centripetal force so let's say tensioner okay tension string somebody tie a string and swing something in a circle okay and one thing you need to know is whatever force this is called is f this always normal to velocity what does normal to velocity means how would you draw the direction of velocity velocity we can draw it as let's say the object is moving here at a certain speed is our tangential or we just call velocity this one is always perpendicular no matter where you are in this circular path okay so maybe i'm down here now draw velocity i still have a force pointing to the center which is perpendicular okay so i'm just leave one here oh my goodness everything disappeared uh the second or the third last point is that this speed this pink color v is constant if your force is constant so if this one is a constant speed that means your force also constant no it didn't get bigger or smaller okay so velocity is one way force is perpendicular lastly force is down to center acceleration also to center this one also pointing to center but velocity is tangential tangential normal is a weird i don't know why they use normal normal means perpendicular a is perpendicular to b a is normal to b right so coming up next we'll look at some basic examples of how to deal with calculations relating force velocity radius and several things like that also called acceleration okay okay no but not bad okay so you can go play some of these simulations to stare at it until you can see the thing moving in the circle in your head okay so that's all for this video i'll see you in the next one