Question

A ballet dancer spins with 24 $rev{s}^{-1}$ with her arms stretched out when the moment of inertia about the axis of rotation is 1. Calculate the new rate of spin, if the moment of inertia about the same axis is 0.61.

• A. 10 rev/s
• B. 20 rev/s
• C. 30 rev/s
• D. 40 rev/s

Answer 1

The correct option is D

40 rev/s

${\omega }_1=24rev/s,I_1=I,I_2=0.61$
According to law of conservation of angular momentum,
$I_1{\omega }_1=I_2{\omega }_{2}I\times 24=0.61{\omega }_2{\omega }_2=\frac{24}{0.6}=\frac{240}{6}=40rev/s$