From the law of conservation of angular momentum, I ω = constant
ω ∞ 1/T, the angular velocity of rotation is inversely proportional to the moment of inertia of the system.
Following are the examples for law of conservation of angular momentum:
(1) A diver jumping from springboard sometimes exhibits somersaults in air before reaching the water surface, because the diver curls his body to decrease the moment of inertia and increase angular velocity.
Fig: A diver jumping from a spring board
When he is about to reach the water surface, he again outstretches his limbs This again increases moment of inertia and decreases the angular velocity. Hence, the diver enters the water surface with a gentle speed.
(2) A ballet dancer can increase her angular velocity by folding her arms, as this decreases the moment of inertia.
Fig: A person rotating on a turn table
(3) Fig. a, shows a person sitting on a turntable holding a pair of heavy dumbbells one in each hand with arms outstretched. The table is rotating with a certain angular velocity. The person suddenly pushes the weight towards his chest as shown Fig. b, the speed of rotation is found to increase considerably.
(4) The angular velocity of a planet in its orbit round the sun increases when it is nearer to the Sun, as the moment of inertia of the planet about the Sun decreases.