Question

A ballet dancer spins about a vertical axis at 75 r.p.m 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.

Answer 1

100

Answer 2

By conservation of angular momentum, $I_1 \omega_1 = I_2 \omega_2$. Using frequencies ($N$), $I_1 N_1 = I_2 N_2$.

Given $N_1 = 75$ r.p.m. and $I_2 = 0.75 I_1$.

Substitute these into the equation: $I_1 (75) = (0.75 I_1) N_2$.

$75 = 0.75 N_2$.

$N_2 = \frac{75}{0.75} = \frac{75}{3/4} = 75 \times \frac{4}{3} = 100$.

The new speed is 100 r.p.m.