Question

A ballet dancer is rotating about his own vertical axis on a smooth horizontal floor. $I$, $\omega$, $L$, and $E$ are the moment of inertia, angular velocity, angular momentum and rotational kinetic energy respectively, of the ballet dancer. If the ballet dancer stretches himself away from his axis of rotation, then,

• A. $I$ increases, $\omega$ and $E$ decrease but $L$ is constant
• B. $I$ decreases, $\omega$ and $E$ increase but $L$ is constant
• C. $I$ increases, $\omega$ decreases, $L$ and $E$ are constant
• D. $I$ increases, $\omega$ increases but $L$ and $E$ are constant

Answer 1

The correct option is A $I$ increases, $\omega$ and $E$ decrease but $L$ is constant

There is no external torque
$\therefore$ Angular momentum , $L=$ constant
$\therefore I\omega =$ constant
The moment of inertia will increase, because mass stretches away from the axis of rotation.
$\therefore \omega$ will decrease.
Rotational $KE$ $=\frac{1}{2}I{\omega }^2$
$=\frac{1}{2}\left(I\omega \right)\omega$
$\therefore$ $KE$ also decreases ($\because I\omega$ is constant)