Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_161

6/161 The elements of a spacecraft with axial mass symmetry and a reaction-wheel control system are shown in the figure. When the motor exerts a torque on the reaction wheel, an equal and opposite torque is exerted on the spacecraft, thereby changing its angular momentum in the z-direction. If all system elements start from rest and the motor exerts a constant torque \(M\) for a time period \(t\), determine the final angular velocity of (a) the spacecraft and (b) the wheel relative to the spacecraft. The mass moment of inertia about the z-axis of the entire spacecraft, including the wheel, is \(I\) and that of the wheel alone is \(I_w\). The spin axis of the wheel is coincident with the z-axis of symmetry of the spacecraft.