Q. A string is wrapped around a uniform solid cylinder of radius r. 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. Note that the positive y direction is downward and counter clockwise torques are positive. Determine the magnitude alpha of the angular acceleration of the cylinder as the block descends.

Express your reply in terms of the cylinder's radius r and the magnitude of the acceleration because of gravity g.