A ballet dancer spins about a vertical axis at 60 rpm with arms outstretched. When her arms folded the angular frequency increases to 90 rpm. Find the change in her moment of inertia.

Explanation

By the principle of conservation of angualr momentum
`Ixx60=I_(2)xx90`
Final moment of inertia, `I_(2)=(2I)/(3)`
Change in moment of inertia `=I-(2I)/(3)=(I)/(3)`
Assuming the initial I to be 100% change in moment of inertia `=(100)/(3)%=33(1)/(3)%`.