A flywheel rotating freely at \(1800 \mathrm{rev} / \mathrm{min}\) clockwise is subjected to a variable counterclockwise torque which is first applied at time \(t=\) 0 . The torque produces a counterclockwise angular acceleration \(\alpha=\) \(4 t \mathrm{rad} / \mathrm{s}^{2}\), where \(t\) is the time in seconds during which the torque is applied. Determine

(a) the time required for the flywheel to reduce its clockwise angular speed to \(900 \mathrm{rev} / \mathrm{min},(b)\) the time required for the flywheel to reverse its direction of rotation, and

(c) the total number of revolutions, clockwise plus counterclockwise, turned by the flywheel during the first 14 seconds of torque application.