 Draw the circle. This delta V is change in the velocity. It is a vector subtraction. It's not the magnitude. Magnitude of change is zero. As it change in magnitude is zero. What I am trying to find here, first I will subtract the two vectors, then I will find the magnitude of the subtraction. Let's try to do that. I will take two points, one point like this. This is one point, point number one and this is point number two. Let's draw this, point number one and point number two. This is velocity V, velocity V. Let's say V1, this is V2. Find the initial velocity, find the velocity. Any doubts? One more thing, one more concession please do. Connect this point, connect that point. This is angle theta. Please look. All of it on V1. This is your time. Have you watched? You watched? You watched it. Guys wake up. I can see that none of you have woke up. You are still in class 10 mode. Class 10 was a relaxation time. Nothing great. I mean sorry to say that, but nothing great you have done in class 10. Even if you score 100%, it does not matter. Your class 10 certificate is your base proof. That's it. Seriously, nobody is going to ask how much have you got in class 10 mode. That's the reality. The sooner you accept and wake up guys, start working hard. Start working hard for your own sake, not for my sake. Please. V1 is like this. This is V1 itself. So this is V2, this is V1. This is V2, this is minus V1. So let me draw it here. This is V2, this is minus V1. The lengths are equal. Can you tell me what is this angle? Theta, all of it. This angle is equal to that angle. This is 90. That is 90. Is 180 or not? And this is 180 minus that. Understood? This angle is theta. And this is also theta guys. The angle between V2 and V1 is theta. What is it? Now tell me one more thing. These two triangles are similar. Theta is same. Yes or no? These two are similar triangles. Understood all of you? So I can take ratio of sides. I can say that the length of V2 minus V1 divided by the length of velocity which is V1. The magnitude of V1 I am calling it as V. Okay? Length of 1 to 2 R, R length 1 to 2 divided by radius R. Yes or no? All of you understood? So the magnitude of V2 minus V1 which is nothing but magnitude of theta V will be equal to R length 1 to 2 into V by R this length. Sorry about that. 1 to 2. Distance 1 to 2. It is not 12. It is 1 to 2. Okay. Distance 1 to 2. Have you understood this? Acceleration is, stop again. Limit delta T tends to 0. Delta V which is distance 1 to 2 V by R times delta T. Okay? So I can take V by R outside because it is constant. Limit delta T tends to 0. 1 to 2 R length divided by distance. 1 to 2 distance. Now tell me if delta T tends to 0, will 1 to 2 coincides with the 1 into R length. So 1 into length 1 into will coincide with the R length. Okay? So in delta T time, what is that distance 1 to 2? If speed is u, delta T speed into time is 1 to 2 length. So when I write this as V into V by R, V into delta T divided by delta T, delta T, delta T gets cancelled. So I am writing it as V square by R. Last one. Last one. Trying to find this limit. Now what I am saying is if delta T tends to 0, it means that time is very, very small. In that time period, the distance 1 to 2 is very small. It is as if equal to the distance the object has travelled, which is along the centre. And distance travelled is, which is what I have written, distance 1 to 2 is speed into delta T. So delta T from the numerator and then it gets cancelled away. So now I am getting it as V square by R. So what we have done is we have derived the formula for this acceleration magnitude. Direction ideal already towards the centre and this is the magnitude. Please write down. V square by R is the centripetal acceleration. This is called centripetal acceleration. V square by R is the centripetal acceleration in tangential velocity, where V is the tangential velocity. So how much force is required to create this much acceleration? So MV square by R force is required. What should be the direction of force? Tangential. Towards the centre. So this force is required, this force is required towards the centre for any object to move in a centre. We are not getting insight too much about what is this force and all. That we will learn in laws of motion chapter. Right now we are just introducing it as, what do you think this force is called? Centripetal force. This is the centripetal force. There is also that we are not doing till now. V square is required to create this centripetal force is centripetal, acceleration is centripetal force. Any doubts? In this chapter our dealing is with respect to acceleration only right now. We will not talk about force.