Q. A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with an angular velocity of $20\ rad/s$. When she stretches her arms fully, the spinning speed decrease in $10\ rad/s$. If $I$ is the initial moment of inertia of the dancer, the new moment of inertia is
A) $2\ I$
B) $3\ I$
C) $I/2$
D) $I/3$
Explanation
(a) Angular momentum of system remains constant
$I \propto \frac{1}{\omega} \Rightarrow \frac{I_{2}}{I_{1}} = \frac{\omega_{1}}{\omega_{2}} = \frac{20}{10} \Rightarrow I_{2} = 2I_{1} = 2I$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.