 acceleration is dv by dt. This is also equal to d square s by dt square in kinematics. So, if the transition is constant, the solution of this equation is what? v is equal to u plus v square is equal to u square plus 2 a s and s is equal to ut plus half dt square. This we have learnt. We will use only when the equation is constant, okay. Alpha is equal to or d of this is equal to d square theta by dt square. Let us now get out the solution of this equation If alpha is constant, we will write down if alpha is constant. Omega is equal to initial end velocity plus omega square equal to omega naught square plus 2 alpha delta theta and more delta theta equals to omega naught t plus half alpha. Things are exactly the same. When you deal with it in algebraic way, it is exactly the same. Not constant then how we used to solve the problem. Use these equations directly. If the equation was given, so here I will write if a is not constant. Similarly here, if alpha is not constant, I will use this equation directly. Are you doing this? Alright. So, let us take a couple of questions and see whether we can replicate what would be this scenario. Fine. There are many equations per second. There is minus of per second square. You need to tell me how many revolutions the object makes before coming to rest. Which formula will you use not to be? Just 0. If I am t and then substitute it later on, there is an equation 0. Initial one is omega. Solutions per second. But is it in this SI units? I need to tell you must go forward in SI units. 10 pi minus pi into delta theta. But delta theta come up. Fifty pi. Getting this? So, how many revolutions? Alright. 2 pi angle is one revolution. Understood? We will stop. It starts spinning in opposite direction. And this acceleration is like that. So, it will stop and then gain angle lost in this direction. Getting it? One more question is right now. The equation is given as 5 minus T per second square. 10 minus T revolutions per second square. It starts from the rest. Initial velocity is 0. You need to find when the angle lost becomes 0 again. So, it becomes 0 again. Not constant. So, I cannot use the reference 5 minus T as it is from 0 to 0. Initial will be from 0 to T. This will be again from 0 to T. So, what you can? 5T minus T square by 2 is equal to 0. If it is 5 minus T equal to 0, you are getting a time when angle acceleration becomes 0. Just because alpha has become 0 does not mean omega is 0. It is like saying that if acceleration is 0, velocity is also 0. It need not be. See what happens is when T is very small, alpha is positive. It will accelerate, T becomes large. It started from angle lost in after some time. So, it is trying to stop it now. So, like this, there are several questions and you will see that solving this question, these type of questions are exactly same the way we have done motion in 1D or motion in 2D. You have done a lot of that. You should equate it. It is exactly same as the way we used to do it earlier. So, you just have to do couple of common practice similar. Fine. So, coming back to the kinematics of rigid body, how do you think the rigid body can move the motion of rigid body? What kind of motion discussed it? It can just stop and move forward. This is translation plus rotation combined. Translation and rotation are combined can also be in a different event. Have you seen is axis moving? The axis is also moving forward with the wheel. If this is the wheel, this is the axis. Right there. When wheel moves forward, axis is moving forward. So, axis can move forward. All right. And have you seen the top plane top? How does it rotate? It rotates like this as well as like that. Yes or no? So, it is axis moving forward. What it is doing? It is axis moving forward. So, I used to make punishment like this. I have not got that kind of punishment ever. So, what happened? How do you think? So, what happened? It was not properly. The center here. Take care. So, the axis of the top is also rotating like this. Yes or no? Right. And when your finger is there, translation plus rotation can happen in different ways. In our syllabus, only one kind of translation plus rotation is there when axis translates. Axis should not rotate. So, like for example, the wheel when it is moving forward, the axis what it is doing is following the straight line path or not. Axis is only translating when the wheel is rotating and moving forward. This kind of motion is there in our syllabus. But not when axis also rotates. So, we can summarize. Change its orientation translation. The line will go straight. Why? Because all the points have the same velocity, same acceleration. Axis is fixed. The real point is not going anywhere. The axis is fixed. And we have just learned that if axis is fixed all with center where on the axis moves forward, it moves forward. It rotates and moves up and down. This is more general motion which is what it typically does this. It is not going in a circle. It is just doing some weird motion. For example, it is probably following this path. It is not a circle motion. Motion in this case. And anyone, how can I visualize the motion? He is saying separate the spinning and translation which is correct in a way. But how can I separate? I mean the process of separating. How will you separate it? I am not asking how can you do it. I am asking how can you separate it? The process of it. It is moving forward. Its axis is fixed. Okay. So, rotation plus translation motion. In rotation plus translation motion, we observe the motion of all the points. We observe the motion of all the points. The motion of all the points related to the center of mass and then add the center of mass motion on it. With respect to center of mass, how it is moving? The mass is velocity on it. Is it total velocity? Yes or no? If suppose I am going forward, I am going forward 5 meters per second. What is the relative velocity? This object will appear to me this one. How it comes? You are subtracting from what you are looking at. Observer sees the world by subtracting his or her velocity. What is the relative velocity? The velocity of object minus velocity of of the center of mass, center of mass total velocity. Understood? Why I am observing the motion of all the simpler circles? With respect to center of mass, everything is moving in a circle because the distance is fixed between any two points. You take any point with you to that point, it will be a circular motion. Because distance is fixed. It is a rigid body. And still I will get a circular motion only relative to that point. All the points motion? Yes. I will get a circular motion only. But why center of mass? Why I am looking everything with respect to center of mass and not with respect to any other point. We already know the location of center of mass, how to find the formula and all. Easy to locate. Second or more important thing, you will understand later on where you will learn about the things. If you do not take the center of mass, if you do not observe with respect to center of mass the pseudo forces act from the center of mass and it will have some torque. To nullify the torque because of the pseudo forces we usually observe with respect to center of mass and then add center of mass as motion on it. And whenever you are confused what to do in this chapter, always follow the center of mass. That is a thumb rule. At times the explanation why the center of mass is not so straight forward but you can use it like a thumb rule. Observe with respect to center of mass what is happening and then add what center of mass is doing. What is it? There will be force, pseudo force will be there. But torque due to pseudo force is missing. Sudo force, torque will be distance from the center of mass will be zero because it is acting from the center of mass.