 we are doing introduction of system of particles and kinematics of its relative body kinematics now we are doing relative body kinematics if you have noticed the first two chapters of the class 11 text book 1 book 1 you have to use the measurement at all after that first two chapters kinematics kinematics right? motion 1 and motion 2 t is what? kinematics fine? the concepts of motion 1 and motion 2 t are combined and put inside the rotational kinematics very good ok and then other two chapters are law of motion and verb energy law of motion and verb energy are called the dynamics of the particle how we can use the law of motion and how we are going to use the one energy concept for a rigid body other motion and as we get verb energy together they combine put in this rotational kinematics fine? we are going to start for law of motion you have force equal to mass mass represent inertia how much amount of force you give to create what amount of acceleration ok larger mass or larger inertia will have lesser acceleration so that is how force is equal to mass and acceleration now translation for example this rigid body is just moving like this is it any different single particle so you can use force equal to mass and acceleration and you don't need any other law to analyze this it starts rotating while moving ok it starts rotating then the angular acceleration also yes or no? but just what causes the translation by the way what causes the translation? force force causes translation so we need to guess now what causes the rotation but before is the rotation inertia against the translation was mass bigger mass acceleration for the same force inertia against rotation is moment of inertia for example let's say you have a big rod one of its ends it is very heavy so rotating from one of its ends you are trying to do that and then rotating from the center which one is easier? center is easier? so it is easy to rotate from the center then from one of its ends so it means what? it means that inertia against rotation is changing depending on from where I am rotating the object yes or no? right? so inertia of rotation itself right? so different axis will have different inertia against rotation so that is the reason why we need to study the inertia against rotation separately because it can be very tricky whereas we never study mass separately in law of motion because mass is very easy to quantify alright? but we need to quantify inertia against rotation properly because at every point different different inertia against rotation is there alright? so the first topic is inertia against rotation and the name of that inertia is called moment of inertia please write down moment of inertia the masses is this sum of m i r i square multiple point masses if there are multiple point masses of a system and the distance the perpendicular distance from the axis of rotation is r 1 r 2 r 3 the moment of inertia is m 1 r 1 square plus m 2 r 2 square plus m 3 r 3 square like that what is r 1 r 2 r 3? perpendicular distance from the axis m 1 m 2 m 3 are the masses for the mass of the point object right? so this is the definition of the moment of inertia any doubt here it is a scalar quantity just like mass it is also inertia it is a scalar quantity you don't need to worry about its direction but yes moment of inertia depends on which axis you are finding it even though it is not a vector it depends on which axis you are finding the moment of inertia anyway let's try to do a small differential of this this is 1 2 3 4 1 kg 2 kg 3 kg 4 kg okay you need to find moment of inertia about this axis where this distance the side of a square is 2 meters central mass is not there no central mass is there what is the answer? any doubt here is the answer m 1 r 1 square plus m 2 i 2 square what is the perpendicular distance of 1 kg? 1 this distance is 1 so 1 into 1 square plus 2 into 1 square plus 4 into 1 square plus 3 into 1 square so add all of that you are going to find kg meters square inertia this is passing through the mass 28 0 0 it passes through the axis perpendicular distance of 4 of 1 kg you have to drop perpendicular from here how much it is? the angle is 2 r 2 let me call this as i 1 and this as i 2 this is i 1 so i 2 will be 1 into moment of inertia 20 20 20 that is it that passes through and through like this 20 finally it will be 1 into plus 2 into 2 square basically it is which is 20 so it is how you rotate this above i 1 what is the sense of rotation how you rotate with i 1 you rotate like this right and axis of the rotating object you curl your fingers in the direction of rotation this is the direction of rotation thumb is the axis