A bug sits on the edge of a rotating disk. Later, the bug begins to move toward the center of the disk. Does the bug exert a torque on the disk?

Answer 1

Sure, The angular momentum of the total bug/disk system has to remain constant since there is no external torque. The moment of inertia of the system decreases, so the angular velocity of the disc increases. There is therefore a tangential force exerted on the disk by the bug's feet :)