Question

prove law of conservation of angular momentum​

Answer 1

hope it will help you

Answer 2

You can consider the torque equation

τ⃗ =Iα⃗ ,

as the rotational equivalent to Newton's second law of motion where torque, moment of inertia and angular acceleration are given by τ⃗ ,I and α⃗ respectively.

Now notice that angular acceleration is the time derivative of angular velocity

τ⃗ =d(Iω⃗ )/dt.

which can be re-arranged into integral form

∫τ⃗ dt=∫d(Iω⃗ ).

Angular momentum L⃗ is given by the relation L⃗ =Iω⃗ . Finally, in Newtonian mechanics, the conservation of angular momentum is used in analysing central force problems i.e. forces in the radial direction. With this is mind, I quote the definition of torque in terms of force

τ⃗ =r⃗ ×F⃗ ,

where the position and net force acting on a body are given by r⃗ and F⃗ respectively. If the force on some body is constantly pointed in the same direction then there is no torque on said body. Hence

C=Iω=L,

and hence,

dL/dt≡0.

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