Meriam, Kraige & Bolton — Plane Kinematics of Rigid Bodies: Problem 5_4

5/4 The angular velocity of a gear is controlled according to \(\omega = 12 - 3t^2\) where \(\omega\), in radians per second, is positive in the clockwise sense and where \(t\) is the time in seconds. Find the net angular displacement \(\Delta\theta\) from the time \(t = 0\) to \(t = 3 \text{ s}\). Also find the total number of revolutions \(N\) through which the gear turns during the 3 seconds.