Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_45

7/45 The gyro rotor shown is spinning at the constant rate of 100 rev/min relative to the \(x\)-\(y\)-\(z\) axes in the direction indicated. If the angle \(\gamma\) between the gimbal ring and the horizontal \(X\)-\(Y\) plane is made to increase at the constant rate of 4 rad/s and if the unit is forced to precess about the vertical at the constant rate \(N = 20\) rev/min, calculate the magnitude of the angular acceleration \(\alpha\) of the rotor when \(\gamma = 30^\circ\). Solve by using Eq. 7/7 applied to the angular velocity of the rotor.