 So, there are a lot of questions on rotational equilibrium. This topic is called rotational equilibrium, equilibrium of a rigid body, same thing. First, let's do couple of questions on finding out torque itself. Listen to this question. Here, it's a heart, that move over the heart. I'm not making it up, see, it is there. What happened? This is 30 degrees. Any other information you need? Where is the axis? Is it in the z direction? Now, let's read it, make it a heart. There's 4, 4, 3, 6. Okay, here's the question. Calculated total torque. So that arrow at the bottom, is that also a force? Yes, that is also a force. 20 newtons, sorry. So, is it 4 meters or a centimeter? Yes, it's a centimeter suddenly. It's hard, it's 4 meters long, it's not that hard. It's 30 degrees. This is the angle 30, this is the arrow. What else do you see? Is there any other angle that can be 30? That's all between 15 and 5. So, it's around 90 degrees. Is it 31? I don't think, that's all. It's an arc, right? Twenty-one, right? Twenty-one, moving up, right? Huh? Twenty-one, maybe, huh? Twenty-one, it doesn't work. Twenty-one, like that. It's 0.31, this way. One point, if the point is right, then it's in right, right. Sir, is it 0.6 or 0.026, whatever it is, tell me sir, 0.2 seconds. No. 1.3, sir. No. Yeah. I don't know which one is right, which one is right. Sir, where is the action? I will do one thing, find out the torque of all the forces one by one. Yes. What you got? Yeah. Torque due to 5 Newton is? Wait. Torque due to 5 is 0, passes through the axis, right. Torque due to 15. How do you get that? 15 to sine 37 is 0.06. What? Sir, you can find a perpendicular distance like this. Guys, you can find the perpendicular distance or you can resolve the forces like that to get the perpendicular. Sir, it's 0.5. Yeah. I am discussing here the solution, so you should pay attention. When I was, you all said something, something, right? I listened and then I am telling you and now you are discussing among yourself, right? Bad manners. What is the perpendicular distance? 6 into? Sine 37. 6 sine 37 is perpendicular distance into 15. 500. 500. 500. Because it is in centimeter. Torque due? Minus 0. Minus 0. Minus 0. Minus 0. Minus 0. You can do plus 1. Minus 0. Minus 0. 10 into 4 divided by 100. What is the point? 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 0. 1. 0. 1. 0. 0. 1. 1. 0. 0. 0. 0. 1. 0. 0. Can you do this. Thank you. Not now. Okay. N-M, that's it, you get the whole number, okay, any doubt, see cause or sign don't remember like that, you need to find perpendicular component of the force which is perpendicular to this line, okay, so this is 60, 20 cos 60 is around this line, right, if you consider this angle 30 then it comes out to be sign 30, sign 30 cos 60, if two lines are like that angle is theta, the component is cos theta times, okay, any doubt, answer is 0.54, please write down center of gravity, definition of center of gravity, center of gravity is different from center of mass, center of gravity is a point, center of gravity is a point which can be considered as if, which can be considered as if entire weight of the object is, entire weight of the object is applied from that point, so earth is pulling the entire object from that single point, if you behave like that, it should be 0, this is like about the center of gravity should be 0, any doubts? Why is the center of gravity not the center of mass, we said it's not always, that is what I was about to do, any other doubt, let us use a definition and find out where the center of gravity lie, this is an irregular shape and size of the object, looks like a car, let us say this is the center of gravity, according to definition entire MG should act from here, entire rigid body is made up of small, small point masses, is there any doubt on that, okay, so let us say this is the point mass of mass M1, so M1g, alright, so M1g, this M1g, there will be M2g, I am splitting the entire mass into multiple masses, this will be M3g, okay, now suppose this distance, this is your R2, this is your R1, this one is your R3, okay, about the center of gravity should be 0, according to definition of center of gravity, torque because of the gravity force, about the center of gravity should be 0, okay, so what it is 1g, let us say g is varying everywhere, okay, it's a big object, gravity is g1, g2, g3, M1g1 plus R, M2g2 and so on divided by, no that's it, equal to 0, direction of g is constant of h, I can write it at like this, M1, direction of g is fixed and if g is constant, let us say, if g is constant, then I can write it as, equal to M2R2 and so on, cross with vector g is equal to 0, this means what, the bracket term is equal to 0, so where the origin is, if bracket term is 0, what summation of, so that summation of M divided by summation of M i is R center of mass, okay, so it is a point, if I multiply and divide by summation of all the masses, this and here is total mass, I multiply and divide by the total mass, okay, so this bracket term is basically, this should be equal to 0, what is 0, 0 is the center of gravity, center of mass, we have assumed, when we started we have assumed, let's say this is the center of gravity, total Mg is applied, let us say and according to the definition, net torque should be 0 about that point, that is what we have done, so it is a point which has M1R1 plus M2R2 and some of all that should be equal to 0, okay and that point is actually the center of mass, alright, so if adjacent due to gravity g is constant throughout the rigid body, then center of gravity and center of mass will coincide, please write down, if small g is constant throughout the rigid body, if small g is constant throughout the rigid body, then center of gravity and center of mass will coincide, then center of gravity and center of mass will coincide, we will stop, of gravity force gravity force on a rigid body gravity force on rigid body can be considered can be considered as a single force as a single force of m into g magnitude m into g magnitude vertically down through the center of gravity fine. So if there is a rigid body capital Mg will be applied through the center of gravity and if nothing is said you please assume that center of gravity and center of mass will coincide because assumption of g being constant for entire rigid body is very common right usually