Rotational Kinetic Energy Practice Test

A rigid hoop rotates about a fixed axis through its center. The hoop’s angular speed is reduced to half its original value, with no change in mass distribution. How does $K_{\text{rot}}$ change?

Two objects rotate about fixed axes with the same angular speed $\omega$. Object X has a larger moment of inertia than Object Y about its axis. Which statement about rotational kinetic energy is correct?