If the motor of Prob. 17-62 is disengaged from the shaft once the flywheel is rotating at 15 rad/s, so that M = 0, determine how long it will take before the resultant bearing friction F = 50 N stops the flywheel from rotating.

Prob. 17-62

A motor supplies a constant torque M = 2 N · m to a 50-mm- diameter shaft O connected to the center of the 30-kg flywheel. The resultant bearing friction F, which the bearing exerts on the shaft, acts tangent to the shaft and has a magnitude of 50 N. Determine how long the torque must be applied to the shaft to increase the flywheel's angular velocity from 4 rad/s to 15 rad/s. The flywheel has a radius of gyration k_o = 0.15 m about its center O.

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25 mm F M -0