2011: Problem 7

Topic: Rigid Bodies
Concepts: Conservation of angular momentum, Kinetic energy

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Solution:

Recall the rotational kinetic energy is given by

$$E=\frac{1}{2}I\omega^2$$

Using the angular momentum $L=I\omega$, we can rewrite

$$E=\frac{1}{2}L\omega$$

In our case, we have conservation of angular momentum since there is no external torque. Since $L$ is constant, we see that doubling the angular velocity also doubles the energy. Thus, the answer is B.

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