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Hello students in this video we’ll discuss about the principles of conservation of Angular Momentum and it is a derivation since let us state and prove the law of Conservation of [Music] stated proof first is the statement conservation of angular momentum means that the population right the statement that I will discuss. you This is a statement in the absence of net external torque the angular momentum of the system will remain same or constant out under so why it is about the options of net external torque because momentum the formula we derived in the last video was I Omega now for the L to be constant with time that I an Omega has to be constant if both are constant because I has to be constant about a particular axis of rotation it doesn’t depend on the how fast the object is rotating it only depends on the body and the given axis as long as the given X is fixed the moment the moment of inertia will remain constant so in this situation the L value is I Omega and out of this I and Omega is constant because I is constant so Omega has to be constant to have this I Omega pencil that means to have L constant if suppose that I is changing and Omega changing then both the changes then also it can have the product constant because one is increasing to decrease and the product will remain constant but in this case that because I is constant of the given axis so about the same X is the Omega has to remain constant so to have Omega constant we to see what influences Omega Omega is influenced by alpha that is angular acceleration so when the where we get angular accelerations we get angular accelerations from top just like we get acceleration from force so we get angular acceleration from top so if Omega is to be constant then alpha has to be 0 that means torque has to be 0 and yeah for then the body is rotating the top value externally have to be do in the absence of net external torque absence is zero so then the net external torque is 0 then alpha is 0 then alpha is 0 then Omega is functioned when Omega is constant then I Omega is function that L is constant so that is the basic idea about the law of conservation of angular momentum now this is the statement and way to prove it so the proof part so in case of this if I consider an object it is rotating with Omega which is constant because I have made it alpha zero and I met top zero this park is also external this is not internal talk because you have talked talking our system the system means it can have one object it can have two objects or it could have any number of objects so the system can be of single object or modifier so when we talk about more than one object suppose two objects and in one studying these two objects if I consider both objects in my system then if one is applying a torque and other or this one is applying a torque on the other object then these talks are not external terms these talks are into the talks so if the internal torques are present then angular momentum that means it doesn’t influence the angular momentum of the system only in the case of external term means if I consider the two of this of my system then no talk has to be applied from outside so as long as internal talks are there that is fine but external term if it is present then that will change Omega of the system and then there is no consideration of angular momentum so the angular momentum has to be constant moly in case of net extra talk zero net external torque means if I apply talks but then if I apply toxins okay actually but if I apply talk in the system in one in clockwise and suppose another anti clockwise sense of same magnitude then also the net value is zero so therefore we talk of the net if a single torque is applied actually that will never be zero so even if the external torques are applied the net hangers to be zero so these are the things now I will prove this what is given if I go by the definition of statement the in absence of net external torque so the nutritional table so what is talk talk is I alpha if this is external torques then this alpha is also external it says that this external torque is zero means that I alpha is zero if I alpha is zero this is given then I write this implies the Omega over DT is zero because this has to be constant now we can do one thing we can take this ie because Omega is constant so I can take PI inside because I is constant can be taken inside or outside if I do that I would have D over DT of I Omega is constant zero this implies that this I Omega is basically L because we have derived last video that it is I Omega so a writer d l or DT is zoom if it is so then the M is 0 DT this implies if I take integration both sides this is L and this is some constant C this would be 0 plus so for fancy this is a constant so what you’re getting is that this is the momentum is constant the C is constant so this gives that L is constant angular momentum of the system will remain constant and therefore this is the proof and again from here you can write one more thing that L is I Omega so I Omega is constant this is what we flew on the system that means before this is constant means I won Omega 1 is I 2 Omega 2 what is the meaning of this momentum angular momentum before and after must be same the initial angular momentum and the final element of what we said for the system so this is the law and of this proof of conservation of angular momentum ok thank you

• ### John Mandlbaur

Dear sir, you proof is mistaken. You assume that I is constant and you assume that dW/dt is constant in order to make your proof so you must maintain those constraints for your final conclusion. The reason that I say this is mistaken is because in a variable radii system (which you imply with your conclusion), I is not constant and neither is W. The fact is that if we measure any variable radii system, we find that angular momentum is not in fact conserved and the results confirm that angular energy is conserved. Please see the examples here: www.baur-research.com/Physics/measure.html

• ### Ekeeda

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