Suppose the time it takes for a wind turbine to rotate triples. By what factor will its rotational kinetic energy change?
A) It will double.
B) It will quadruple.
C) It will decrease to 1/9 its original value.
D) It will increase to 9 times its original value.

Question

Quizplus · Accepted Answer

The rotational kinetic energy of an object is given by the formula $E_k = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. If the time for one rotation triples, the angular velocity decreases to one-third of its original value ($\omega \rightarrow \frac{\omega}{3}$). Substituting this into the kinetic energy formula gives $E_k = \frac{1}{2}I\left(\frac{\omega}{3}\right)^2 = \frac{1}{2}I\frac{\omega^2}{9} = \frac{1}{9}$ of its original value, hence the kinetic energy decreases to 1/9 of its original value.

Suppose the Time It Takes for a Wind Turbine to Rotate