A string is wrapped around the edge of a uniform disc, and its free end is attached to the ceiling. The disc descends, unwinding the string. Determine the downward acceleration of the disc.

Step-by-step solution

Let M be the mass and R be the radius of the uniform disc. Let a be the downward acceleration of the center of mass and be the angular acceleration of the disc. Since the string is attached to the ceiling and unwinds without slipping, the point of contact has zero acceleration, which gives the constraint equation: a = R The forces acting on the disc are its weight Mg downwards and the tension T upwards. The equation of translational motion is: Mg - T = Ma The torque about the center of mass is provided by the tensi