Work Step by Step
There is no external torque, so the angular momentum is conserved, i.e., remains constant. The magnitude of the angular momentum is the moment of inertia multiplied by the angular speed, $L = I \omega$. A shorter string brings the mass closer to the axis of rotation and reduces the moment of inertia of the system. To compensate and to keep L the same, the angular speed $\omega$ must increase.