In Example 10.10 (Section 10.6) the rotational kinetic energy of the professor and dumbbells increases. But since there are no external torques, no work is being done to change the rotational kinetic energy. Then, by Eq. (10.22), the kinetic energy must remain the same! Explain what is wrong with this reasoning that leads to this apparent contradiction. Where ?does ?the extra kinetic energy come from?

Step 1: The kinetic energy of the professor and dumbbells increases as he pulls his hands near his chest. The increase in kinetic energy does not require the external torque or work. When the professor pulls his hand the moment of inertia...