A motor supplies a constant torque M= 2 N • m to a 50-mm-diameter shaft O connected to t...

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.