 without slipping. Circle, cylinder, sphere, all these can roll. So basically the cross action should be what? Circular. When you look at from front, only these orchestras can roll. Axis moves up and down. That is not in our syllabus. Okay, axis should translate. Only the circular cross action has a rolling in our syllabus. So when you see a rolling object, suppose it is rolling on a surface like rolling will be. Yeah, suppose it will be on the surface. So it will have some velocity. Yes or no? And the center of mass will also have some velocity. That is a B. Center of mass will move forward or not? Yes. Right. And what is the condition for this rolling? There should not be any slipping. The first little distance, when slipping happens. When the slipping happens? I suppose you have two objects in contact like this. When the slipping will happen. Right, no slipping is happening. No slipping is happening. So for slipping. I suppose it will lose contact. Suppose they move my two hands together. No slipping means that relative velocity between the two surfaces is zero. No slipping is a condition in which at a point of contact, at the point of contact zero, wherever it is having a contact, the velocity zero means what? The velocity of one surface is equal to the velocity of the other. So at a point of contact, the velocity of the object should be equal to the velocity of the surface. So what happens? Inclined plane will be at rest. So most of the time surface will be at rest. So what should be the velocity of no slipping? Zero. So it should be zero if there is no slipping. Got it? Which point is in contact for this object? This point is in contact. And what is its total velocity? You seem lost today. What are you thinking? What is the velocity of this point of contact? He is telling you which is not correct. Okay, whatever he is saying is not correct. Apply your thoughts and tell me what is the answer. Point of contact velocity is what? It is the velocity of the point of contact. Come, come, sit front. You are not paying attention. I am worried. Stay worried in my face. Pay attention. You are not going to learn this anywhere easier. Okay? If you don't pay attention here, they said don't pay attention. You will never learn this. And I have seen it past 10 years. I have seen this. What is the velocity of point of contact? r omega minus v. r omega this may be zero. This should be equal to zero. So v will be equal to in the surface at rest. For no slipping, v should be equal to r omega. For no slipping, v should be equal to r omega. If the surface is at rest, what kind of surface it is? Inclined surface, horizontal surface, vertical surface doesn't matter. v will be equal to r omega. If the surface is at rest, what about with respect to acceleration? Suppose acceleration is a and angular acceleration is alpha. It is a differentiated. We get a is equal to r alpha. Ready? So these are the conditions for it to not to slip. They are like constraint relations, which have nothing to do with physics actually. It is mathematical constraint. Suppose the object is rolling without slipping, this should be true. Okay. So till now, till now there was no relation between vcm and omega. vcm can exist independently and omega can exist independently or whatever value of each. But it has to do the zero problem without slipping. There is a condition between vcm and omega. First time they are constrained to have a relation. Very good. All right? Similarly with acceleration k is equal to r omega. Now what if the surface in contact is not at rest? Suppose this is kept on this, which is moving with velocity v1 and attrition is a1. Can you tell me what is the relation now? Break it down, break it down. What kind of punishment do you get in school? Like suppose the teacher of punishment. I mean it is some kind of torture. My teacher used to hit me. He used to come and slap me for no reason. So he was teaching some chacha nehru and all that. So just fine. I was sitting in the front desk. Probably I was talking. So he just came and like what? So I mean nowadays all these are not going on. But what is popular nowadays? What is trending? Standing on chair table on a groupie thing. Like influence and then thank you. And you do they make you more or less do one thing. So that's level one punishment we all, we all tend to do this now. That level one punishment is stand on the desk. Level two is get out of the way. It should be embarrassing. Level one is standard. Level two is as in level three is become a murga and you'll see a murga soon. What do you know how to do? So level three and murga is also two or three times. You have to, I mean books one times. And when we tell our parents and my teacher as our parents are like take off. Because we as a student might have done something that is why our parents will think like that. So we never used to tell. What else? I still remember I don't know what I have told you this. One day our lab assistant was not present because of me. I told you. So he appointed probably that point in time the social science teacher who was my favorite teacher was available that point. So you were like, okay, please take care of these kids enough in a lab only we're sitting and this thing was doing his work. And you know kids like when I was kid and you and you're not at your age. It was when I was in class nine. So if you just tell us to sit without doing anything, that's the hardest thing to do. I mean, suppose you're making noise, I tell you to write this definition that you keep quiet. So you'll never be sick. So we'll make noise. So he came and he didn't beat me that. I still remember that. Okay. But then he has to go. So I found them in Facebook something like this. R-minor should be 6 should be equal to velocity of surface at the point of contact. What about a-r-r will be equal to a1. Just one more scenario. You can scale punishment. That's it. Got it? Same thing? Most sensible question. He got it. This is cool only. He got it. It's cool only. Same yourself. He got it wrong. And how that? I don't know. I don't know. Have you gone kneel down? Kneel down. Conditions for that. What is that? How the variables are related. Who is probably? The point of contact should have the same acceleration as that of this surface in contact. What is the acceleration of this point? Alpha r a, this should be equal to what? a2. What about the acceleration of this point? a-alpha r that way. This should be equal to a1. Okay. I will tell you one thing. The point is instantaneously I rest instantaneously. I rest with respect to the surface. I rest instantaneously. Okay. Suppose friction is acting on it. Can friction do any work? Every instant the displacement is by the friction. Work done by the friction in pure rolling is zero. And the friction force in the pure rolling is zero. This we are going to use it later. Okay. Eight outs in the entire kinematics. This is the kinematics of rigid body. Eight outs in the entire kinematics. So please solve 50 to 60 questions on kinematics that you feel at ease with this topic. You got it? 50 to 60. That's like medium up. And how much time did it take? 50 questions? How much time? 50 to 60. Max to max 3 hours. Max to max 3 hours. How many questions you write in the chemo test? 90 questions. Around 19, 3 hours? Now this end is right. Earlier it was 19. Right? That's it. I am not saying you should take it right. In order to attend the question, the question will hardly take 2 hours for 3 hours. Okay. So don't count 50 questions as if I am telling you 50 hours. Okay. And this is like minimum thing. Minimum required thing for in next chemo test. Now itself. Now itself. All right. Okay. I felt sick again. I knew it. I could come for the whole hour again. I felt sick again. Stay tuned. All right. Pay attention here and write on the chemo test. The next chemo test must prepare now onwards. Let me tell you. Listen here. If you are removing school marks, it is easier for you to remove the computer exams marks and so on. So if suppose one UT, let's say one UT, you don't prepare that. That is probably what our parents may use to think because their bank-on-the-bank scenario was different. Now scenario has changed. Okay. So it is our duty to make them aware of the kind of scenario we are in. It is class 12 board. They've got 96, 97 percent. Okay. It's easy. It's very easy. Are you getting it? If you don't score well in terms of this chemo test, not score so well till now in the any of the chemo test. And ultimately, this is what will make you go to the some good college. Okay. There are scores in these kind of exams. So do a favor to yourself. Prepare for chemo test only until the next chemo test. Okay. I'll give you a best shot. Don't just get involved in the work related to some monotonous thing like completing the lab records, all those things. Do it in the school itself. All those lab records completed in the school. Find time somewhere sneaky there and there. Completed in the actual standard case. You can imagine the kind of work they have done till now, starting from the day one of class 11. And they're talking in school as well, on top of it. They're doing every work. They're still in time. Okay. There are some kids who are doing x-ray well in bio, physics, chemistry, maths, everything and everywhere. So it is not about time. It is about how much derivative you are towards a simple cost. Okay. You can improve your school marks easily, but not to commentate about exams. Anyway, so this is rotational kinematics and this is done.