## Physics: Principles with Applications (7th Edition)

The KE can be written in terms of the angular momentum ($L = I \omega$) and the moment of inertia of the block ($I = md^{2}$, where $d$ is the radius of block’s path): $$KE = \frac{1}{2}I \omega^2 = \sqrt{\frac{L^2}{2 I}}$$ As in the previous problem, there is no external torque, so the angular momentum L is conserved, i.e., remains constant. A shorter string brings the mass closer to the axis of rotation and reduces the moment of inertia I of the system. We see that the KE of the block increases, so the block is moving faster.