State the law of conservation of angular momentum and explain with a suitable example.

Explanation

`(ii)` Law of conservation of angular momentum : The angular momentum of a body is conserved if the resultant external torque on the body is zero.
Explanation : Consider a person hodling weights seated on a platform that can rotate freely about a vertical axis. Let, the platform be set into rotation at an angular speed `omega_(1)` with the person holding his arms close to his body. When he extends out his arms horizontally, the moment of inertia of the system increases from its intial value `I_(1)` to a larger value `I_(2)`, because the weights are now further away from the axis of rotation. Since his angular momentum is conserved, his final angular speed, `omega_(2)=omega_(1)((I_(1))/(I_(2)))`. Because `I_(2) gt I_(1)`, `omega_(2) lt omega_(1)`. Hence, his speed of rotation slows down.