Question

A ballet dancer spins about a vertical axis 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.

Answer 1

We have,

Angular speed $\omega =90rpm$

Let the initial moment of inertia $=I$

$75\%$ of this $M.I=\frac{3}{4}$

Let the new angular speed be ${\omega }_0$

According to law of conservation of angular momentum,

$\frac{3}{4}I{\omega }_0=I\omega$

$\frac{3}{4}{\omega }_0=90$

${\omega }_0=90\times \frac{4}{3}$

$=120rpm$