State and prove the principle of conservation of angular momentum. Explain the principle of conservation of angular momentum with examples.

Statement: In the absence of an external torque the total angular momentum of a system remain constant.
Proof: By definition, the rate of charge of angular momentum is called Torque.

Examples:

1. When a man with stretched out arms stands on a turn table which is revolving then his moment of inertia is high. If he folded his hands, the moment of inertia decreases and hence the angular velocity increases. In both cases angular momentum remains constant.
2. All helicopters have two propellers. In case a helicopter has one propeller, it will itself rotate in the opposite direction in order to conserve angular momentum. As the rotor of the main propeller at the top of helicopter starts rotating, the body of the helicopter has a tendency to rotate in the opposite direction. This tendency is counter balanced by a small propeller provided in its tail.