A string is wrapped around a uniform solid cylinder of radius r, as shown in the

Question

A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure . 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 counterclockwise torques are positive. Find the magnitude alpha of the angular acceleration o f the cylinder as the block descends. Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

Explanation / Answer

for the cylinder: T*r = I* = mr2/2 *   so T = mr/2     (1) for the block: mg - T = ma = mr    (2) (1) + (2): mg = 3mr/2 = 2g/(3r)

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