Suppose the moon's angular velocity is halved. By what factor will its rotational kinetic energy change?
A) It will double.
B) It will quadruple.
C) It will decrease to ¼ its original value.
D) It will decrease to ½ its original value.

Question

Quizplus · Accepted Answer

The rotational kinetic energy is given by $ \frac{1}{2}I\omega^2 $, where $I$ is the moment of inertia and $ \omega $ is the angular velocity. If the angular velocity is halved, the kinetic energy becomes $ \frac{1}{2}I\left(\frac{\omega}{2}\right)^2 = \frac{1}{2}I\frac{\omega^2}{4} = \frac{1}{4}\left(\frac{1}{2}I\omega^2\right) $, which is a quarter of its original value.

Suppose the Moon's Angular Velocity Is Halved