Question

A ballet dancer spins about a vertical axis at 90 rpm with arms outstretched. With the arms folded. the moment of inertia about the same axis of rotation changes to 75%. Calculate the new speed of rotation.

(Ans: 120 rpm)

Answer 1

Given:

Angular velocity = 90 rpm

Moment of inertia = 75 %

To find:

The new speed.

Solution:

By the law of conservation of angular momentum,

3 / 4 ( Inertia ) New angular velocity = Inertia * Angular velocity

Substituting,

And cancelling Inertia on both sides,

We get,

3 / 4 New angular velocity = 90

New angular velocity = 90 * 4 / 3

New angular velocity = 120 rpm