A motor supplies a constant torque M = 2 N m to a 50-mm- diameter shaft

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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 ko = 0.15 m about its center O.

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