Alphymus

An ice skater can rotate about a vertical axis with an angular velocity $\omega_0$ by holding her arms straight out. She can then pull in her arms close to her body so that her angular velocity changes to $2\omega_0$, without the application of any external torque. What is the ratio of her final rotational kinetic energy to her initial rotational kinetic energy?

(A) $\sqrt 2$
(B) $2$
(C) $2\sqrt 2$
(D) $4$
(E) $8$