Meriam, Kraige & Bolton — Plane Kinematics of Rigid Bodies: Problem 5_149

5/149 The frictional resistance to the rotation of a flywheel consists of a retardation due to air friction which varies as the square of the angular velocity and a constant frictional retardation in the bearing. As a result the angular acceleration of the flywheel while it is allowed to coast is given by \(\alpha = -K - k\omega^2\), where \(K\) and \(k\) are constants. Determine an expression for the time required for the flywheel to come to rest from an initial angular velocity \(\omega_0\).