Newton's second law:
Angular and linear accelerations are related by:
Moment of inertia for a cylinder:
Torque in terms of angular acceleration:
Substituting for the moment of inertia and the expression of torque:
A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure (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. Note that the positive y direction is downward and counterclockwise torques are positive.
Find the magnitude α of the angular acceleration of 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.
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