Law of conservation of angular momentum states that in the absence of an external torque, the total angular momentum is conserved or the total angular momentum of an isolated system remains constant both in magnitude and direction. If ω1 is the angular velocity when the moment of inertia is I1 and ω2 is the angular velocity when the moment of inertia is I2, then from the law of conservation of angular momentum it follows that I1 ω1 = I2 ω2
Examples:
1. A spinning ballet dancer uses the principle of conservation of angular velocity to increase her angular velocity. She first spins her arms and one of her legs. The moment of inertia about the axis of rotation is large. Consequently, her angular speed is small. She then folds her arms and brings the stretched leg closer to the ther leg. As a result of her moment of inertia about, the axis of rotation decreases and her angular speed increases.
2. A diver jumping from a springboard folds his arms and legs inwards and curls his body. As a result, his moment of inertia decreases. He then somersaults in the air with a large angular speed. Just before touching the surface water he stretches his limbs. His moment of inertia increases. Consequently, his angular speed decreases. He thus strikes water with lower speed.
