 Alright so today start with kinematics of the rigid body, fine? Please write down and change its volume. Is water the rigid body? It's all basically, okay? A rigid body is a hypothetical object, right? Such object do not exist but approximately we can say that any solid behaves like a rigid body, right? Please write down in a rigid body, a rigid body is an object, a rigid body is an object which do not get deformed, right? Which do not get deformed. Now in reality every solid if you apply some force will have a stress because of that strain will be produced and there is a deformation, alright? But we will assume that the forces are so less, so little that the deformation is needed. For example if I stress this television from left hand side there is slight deformation but that is negligible. We is so less that we can ignore it, alright? Now this is what the rigid body is, whatever you have written, okay? But mathematically how can you, a rigid body is something which do not get deformed, alright? Say this in a mathematical way. Suppose I take two points on the rigid body, the attention infinity but again I am telling you the way you should tell me, okay? Tell me with respect to the two points on the rigid body. What should happen between the two points on the rigid body for it to be a rigid body? What? The distance between any two points on the rigid body is fixed. This right now, distance between any two points on the rigid body is fixed. Distance between them neither increase nor decrease, alright? So suppose you have point A and this is point B. Distance between them is suppose 20 centimeter. It will remain 20 centimeter no matter what the rigid body does. If it changes then essentially rigid body is getting deformed and then you can't call it a rigid body, right? Is this a rigid body, this pen? Is it? The distance between the points are changing. Take a point over here on the cap and take a point over here. These two points, when I rotate that point goes backwards, so distance is changing. So as I know, if distance between the two points is fixed, can one point move relative to the other point? Is it possible? What are you doing here? I am saying that if distance between the two points is fixed, like the case in the rigid body, can they move relative to each other? They can move. Isn't the tip that distance should remain same? So what is the possible path of relative velocity? It should move in a circle so it will move in a circle like this. Keeping the distance fixed all the time. Same way all the points on the fan. So please write down the rigid body every circle with respect to every other point. And center is also moving in a circle with respect to center. All are relatively simpler if it is not random shape and size of a rigid body. And suppose this rigid body rotates. If this rigid body rotates, let's observe what are the points doing. I am taking point 1, point 2 and point 3. So this line represents the axis of rotation. About this axis, this object is spinning. Find just like fan is spinning. That's all. Now can you tell what is happening with the point number 1 when it rotates? It is moving in a circle. So this point number 1 moves in a circle like this. What is happening with point number 3? This is also describing a circle. Point number 2 also moves in a circle like this. So basically the axis is got locus of all the centers. As you know, all the circle motions center lie on the axis. Now tell me one thing. If this point 1 completes one full circle in 2 seconds. How much time point 3 will take to complete the full circle? 2 seconds only? If it takes less or more time, what will happen? Then the twisting will happen. Twisting happens for rigid body. So it will get deformed. So all the points should move by same angle at same time. Please write down all the points on the rigid body. The body should rotate by same angle at the same time. It is a rigid body. If it is not a rigid body, all of these are not valid. So all the points rotate by same angle at the same time. All of you understood this? Now tell me the speed of point 1 is more or point 3 is more? What is more reason? It has to travel a bigger distance. Same amount of time. Getting it? So because very difficult to in terms of distance, speed and acceleration. Because there are infinite points. All those infinite points will have infinite velocity and acceleration. Distance travel. Getting it? So that is the reason why we do not use distance, velocity and acceleration when we are analyzing a rigid body. But the property of rigid body that they will all move same angle at the same time makes variables handy when you analyze the rigid body. Rather than displacement, you try how much angle they have moved. It will be same for all particles. Rather than velocity, you are tracking what is the rate at which angle is changing. Which is angular velocity and angular acceleration. So we are tracking angular acceleration when we are dealing with rigid body. But finally I should know that if I know what is the angular velocity. I must know what is the relation between angular velocity and the linear velocity or the actual velocity. Because ultimately kinetic energy when you write it is half MV square. But ultimately all the formulas are in terms of velocity, acceleration and displacement. So let us first see what is the relation between the angular variables. What are the angular variables? Angle, angular velocity and angular acceleration. And what is the relation between the angular variable? Now tell me if this point 1 has 7 at angle of delta theta. How much distance the point 1 has moved? Let us say this radius is r1. How much distance? Take a circle like this. If point 1 has gone from this point to that point. This angle is delta theta. This is angle is r1 delta theta and divided by radius is angle. So I will take this. Theta angle corresponds to r1 delta theta distance. What is the assumption here? The assumption is that the rigid body is staying at one place and rotating. If it starts moving and rotating. If it starts to move as well as rotate. Then this is not a tangent angle. Are you getting it? Right now we are dealing with fixed axis. The axis is fixed. Or you can say that it is spinning. This is angular variable. This is not distance term. Delta s you can say. If at which angle is changing. It is referred as angular velocity omega. We have done this in several motions. Yes or no? Something similar we have done already. Distance changes. Whatever. So this is angular velocity to differentiate this. Won't you get ds by dt? Differentiate distance you will get. Spin. Yes or no? So differentiate it r1 is constant. So r1 comes out. So it is d theta y. This is my velocity at any point in time. Which is r1 into omega. We have done this earlier also. And there is something called angular acceleration. d omega by dt is alpha. So this is my velocity. So if I differentiate velocity I will get acceleration. d by dt is r1 into d omega by dt. Which is r1 alpha. So if I know omega at any point in time. If I know the distance from the axis. If I know angular time I will get. The interaction of a point whose distance from the axis is r1. What is this r1? r1 r2 r3 are the perpendicular distance from the axis. There are not any distances. You should find out the perpendicular distance. So if I know the angular variable at any point in time. If I know theta. I can easily know what is the distance favorite. What is the velocity and what is the acceleration. Yes or no? Distance velocity and angular acceleration. I will keep a track of angle, angle velocity and alpha. Because it is easier to keep track of these. There will be final point of the rigid body. I will keep track of all of their velocity. All of their acceleration and distance. Are you getting the point?