A ballet dancer spins about a vertical axis at 100 rpm which arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes to 80% of its initial value.
Calculate the new frequency of rotation.

Explanation

Data : ` f_(1) = 100 "rpm" , I_(2) = 0.8 I_(1)`
By the law of conservation of angular momentum `I_(1)omega_(1) = I_(2) omega_(2)`
` I_(1)(2pif_(1)) = I_(2)(2pif_(2))`
`f_(2) = (I_(1)/I_(2)) f_(1) = (1/0.8) = 100 = 125 " rpm"`
The gives the new frequency of rotations.