Irodov Problem 1.193

Since the thread is being pulled in with constant speed, there is no radial acceleration. The only radial acceleration seen by particle is thus the centripetal acceleration as a result of its rotation. This is completely provided by the tension in the string T. Hence,


Now since the only force acting on the particle is T and us always acting radially inwards, there is no torque acting on the disc as seen from the center of rotation (the hole). In other words the angular momentum as seen from the hole will always be conserved. Hence we have,