Suppose the time it takes for the moon to rotate doubles. 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 the formula $KE_{rot} = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. If the time for one rotation doubles, the angular velocity is halved. Since the kinetic energy depends on the square of the angular velocity, halving $\omega$ results in the kinetic energy becoming one-fourth ($\frac{1}{2}^2$) of its original value.

Suppose the Time It Takes for the Moon to Rotate