State conservation of angular momentum.

Explanation

Law of conservation of angular momentum states that when no external torque acts on body, the net angular momentum of a rotating rigid body remains constant.
`tau=(dL)/(dt)`
If `tau=0` then `L=` constant ……….1
AS the angular momentum is `L=I omega`, the conservation of angular momentum could further be written for initial and final situations as,
`I_(i)omega_(i)=I_(f)omega_(f)` or `Iomega=` constant....2
The equations 1 and 2 say that if I increases `omega` will decreases and vice versa to keep the angular momentum constant.

Eg: The dancer spins slowly when the hands are stretched out and spins faster when the hands are brought close to the body. Stretching of hands away from body increases momnet of inertia, thus the angular velocity decreases resulting in slower spin. When the hands are brought close to the body, the moment of inertia decreases, and thus the angular velocity increases resulting in faster spin.