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?
Answer Choices
A. \sqrt{2}
B. 2
C. 2 \sqrt{2}
D. 4
E. 8