 of this point. What will be this velocity? We have to add 60. So, this is 60 degrees that is that. This is vcm and this is vcm by 2 and this angle is 60 degree. Can you find out now? Total velocity will be 2 into vcm square by 2 cos of 60. This is root over vcm square plus vcm square by 4 plus vcm square by 2. How much is this? What? vcm root 7 by 2. You first observe with a precto centromass and then add or find a total loss. Let us see with acceleration what we can do. To find the acceleration of these 4 points quickly minus a centripetal acceleration we are ignoring. We are ignoring centripetal acceleration. All of you understand this? There will be centripetal acceleration also. Fine. For that I need to know the velocity v square by r. The centripetal acceleration will be 2 at this point. What about centripetal acceleration at this point? How much will be this direction? Radial is that direction. This point tangential is alpha into r. Radial is a plus v square by r. There are small nuances you have to take care when you deal with anything. I am just telling you how you can analyze if something comes like this as a problem. Can you doubt? Next we will go down the cylinder. Axis moves up and down. Axis should travel section as a rolling in our cylinder. So when you see a rolling object, suppose you are going to be on the surface. So centromass will also have some velocity. The condition for this rolling, they should not. Now first let us discuss when we have this. The condition is not there. It will lose contact. No slip in. What is the condition in which no slip in is a condition in which at a point of contact, the point of contact 0. Having a contact relative velocity 0 means what? The velocity of one surface is equal to the velocity of the other. So at a point of contact velocity 0. Fine. Okay. So, what I was saying? Correct. So most of the time surface will be addressed. So what should be the velocity for no slipping? 0. If there is no slipping, got it? This point is in contact and what is its total velocity? What is its velocity? What are you thinking? So, what is the velocity of this point of contact? V plus. He is telling you which is not correct. Okay, whatever he told you is not correct. Apply your thoughts and tell me what is the answer. Point of contact velocity is what? Zero. In terms of V and R, I went to either a Come sit front, you are not paying attention. I am worried. Say you are worried in my face. Any way is easier. If you don't pay attention here, listen. Don't pay attention. You will never learn this and I have seen it. For the past 10 years I have seen this. Got it? What is the velocity? R omega minus V. Zero. This should be equal to zero. We write down if the surface is 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. Doesn't matter 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. You just differentiate it. If A is equal to R alpha. So these are the conditions for it to not to slip like constraint relations which have nothing to do with physics actually. It is mathematical constraint. Suppose the Vcm and omega. There is a condition between Vcm and omega. First time they are constrained to have a relation. Similarly with acceleration A is equal to R alpha. Now what if the surface in contact is not at rest? Suppose this is kept on this which is moving with velocity V1 and acceleration is A1. Can you tell me what is the relation now? Write it down. Why shouldn't you get in school like suppose the teacher is a punishment? Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. Charge. it should be embarrassing level one is essence level three is become a murga and you will see a murga soon murga you know how to do i am just here show i will help you so i mean come talk thank you thank you that is why i would like you to think like that from here to there so we never used to tell otherwise at home also what else i still remember one day our lab assistant was not present he was on leave i told you so he appointed probably that point in time the social science teacher who was my favorite teacher was was available that point in time so he was like please take care of these kids in a lab only we are sitting and this guy was doing his work you know kids like when i was kid and you at your age not at your age it was when i was in class in my so if you just tell us what to do i mean suppose you are making noise i will tell you keep quiet so we will make noise so he came and he didn't beat me that day very hard and i still remember that okay but then he has gone i found them in facebook sometime oh no logical a minus r alpha r scenario wooden scale punishment i said got hit anyway who is calling you no no this is for only you send yourself i just had you don't have any story but listen to my dad got hit my mom got hit he got hit so he has something to share they share it with everyone there is something to bear this is even if you make noise yes somehow girls never got such punishment say that as well she used to pick the but adam was nice no no no no no no no no no no no no no no no no no no no What is the equation? A, this should be equal to what? A2, what about it? A minus alpha that way. This should be equal to A1, okay. Fine. I will tell you one thing, the point of contact is instantaneously at rest, related to the instantaneously at rest with respect to the surface. Point of contact is at rest instantaneously, okay. Most friction is acting on it. Can friction do any work? Every instant by the friction work done by the friction in pure rolling is zero. Work done by the friction force in the pure rolling is zero. This we are going to use in the entire kinematic. This is the kinematics of rigid body. Any doubts in the kinematics? So please solve 50 to 60 questions on kinematics, then you will feel at ease with this topic. Got it? How many? 50 to 60. That's like minimum. And how much time will it take 50 questions? How much time? Max to max 3 hours. Max to max 3 hours. How many questions you will make? Now it is 75, right? In order to attempt the question, I am not saying you should take it right. In order to attempt the question, 50 questions will hardly take 2 hours or 3 hours. Okay? So don't count 50 questions as if I am telling you 50 hours. Okay? Now itself. All right? I felt sick again. Be careful. Be careful. All right. Pay attention. I called the K-1 test. And next K-1 test you must prepare now onwards. Let me tell you, whatever it is, something is said here. What do you say? What happened? How? Oh, so you are surprised that we got so much or so less. Listen here. Listen, listen, listen. In fact, improving school marks is easier or improving the computer exams. So if suppose one UT, let's say one UT, you don't prepare a 697 percent. Okay? It's easy. It's very easy. Are you getting it? If you don't score well, most of you have not scored so well in K-1 test. And ultimately this is what will make you go to some good college. Okay? There are scores in these kind of exams. So do a favor to your test only until the next K-1 test. Okay? And give your best shot. Don't just get involved in the work related to some monotonous things like completing the lab records and all those things. Do it in the school itself. All those lab records complete in the school. Find time, some days meet you there. Complete it. You can't imagine the kind of work they have done till now. Starting from the day one of class 11. And they are topping the school as well on top of it. They are doing every work. They still wait time. Okay? They are everything and everywhere but towards a simple goal. Okay? You can improve your school marks easily but not the computer level exams. Anyway, so this is rotational kinematics and this is done. Now itself. Just now. Before this, we were doing introduction of system of particles and now we are doing budget body dynamics. The first two chapters of the class 11, text book one, book one. You have a unison measurement now. After that, first two chapters. Kinematics. Kinematics, right? Motion went inside the rotational kinematics. The concept for a rigid body. Together they combine, put in this rotation dynamics. What is mass? Mass represented, mass represented inertia. How much amount of force you give to create what amount of acceleration? Okay? Larger mass acceleration. So that is the acceleration. For example, this rigid body is just moving like us rotating while moving. Okay? If it starts rotating then you need to take into an also. Yes or no? Not just what causes a translation. By the way, what causes a translation? Force. Force causes a translation. Inertia against rotation is moment of which one is easier? Center is easier. So it is easy to rotate. It means that inertia against a rotation is changing depending on from where I am rotating the object. Yes or no? We need to study the inertia against the rotation separately because it can be very tricky. Whereas we never study mass separately because mass is very easy, right? Easy to quantify, right? But we need to quantify inertia against a rotation properly because at a rotation is there. And the name of that inertia is called moment of inertia. Please write down moment of inertia. This is the sum of mi ri squared. The mass is, if there are multiple point masses of a system, m2 r2 squared plus m3 r3 squared. Like that. Are you getting it? What is our own object? So this is the definition. It is a scalar quantity. Just like mass, it is also inertia. It is a scalar quantity. You have to worry about its direction. But yes, moment of which axis you are finding it. Even though it is not which axis you are finding the moment of inertia. Dedicate a small numerical of this. 2, 3, 1 kg, 2 kg, 4 kg. This is axis where this of a square is 2 meters. That was 4 into 1 square plus 3 into 1 square. 2 r2. 2 r2. So this is 2 square. So basically it is. So it is more diffs above I1. What is the sense of rotation? How it will rotate with I1? It will rotate like this. Can be other than this distribution of mass. Sharing of mass. Tell me an example of continuous distribution of mass. Till now we are dealing with discrete masses. What is the discrete mass? It is not a point mass. So how do you find moment of inertia of this continuous mass distribution? That is what we are going to do now. You remember center of mass of continuous mass distribution? Remember that distributed each. And let us say its distance from the axis is r2. So dm r2. Summation I have to do. So this summation becomes integral. For a continuous mass.