A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1). The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.Find the magnitude a of the angular acceleration of the cylinder as the block descends.

Rotational Motion:

If a torque of magnitude τ is applied on a rigid body, then the rigid body will start rotating with an acceleration (α ) given by the equation, τ=Iα, where I is the moment of inertia of the of the rigid body about its axis of rotation.