A string is wrapped around a uniform cylinder of mass M and radius R. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar (Fig. P8.84). Show that (a) the tension in the string is one-third the weight of the cylinder, (b) the magnitude of the acceleration of the center of gravity is 2g/3, and (c) the speed of the center of gravity is (4gh/3)1/2 after the cylinder has descended through distance h. Verify your answer to part (c) with the energy approachFIGURE P8.84.

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A string is wrapped around a uniform cylinder of mass M and radius R. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar (Fig. P8.84). Show that (a) the tension in the string is one-third the weight of the cylinder, (b) the magnitude of the acceleration of the center of gravity is 2g/3, and (c) the speed of the center of gravity is (4gh/3)1/2 after the cylinder has descended through distance h. Verify your answer to part (c) with the energy approach

FIGURE P8.84

 width=.

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