One end of a straight rod is fixed at a point O on a smooth horizontal table and the rod is made to rotate around O with constant angular speed Ω. A uniform circular disk of radius a lies flat on the table and can slide freely upon it. The disc remains in contact with the rod at all times and is constrained to roll along the rod.
Initially, the disk is at rest (relative to the rod) with its point of contact at a distance a from O. Find the displacement of the disk as a function of the time.