The elements of a spacecraft with axial mass symmetry and a reaction-wheel control syste...

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 The spin axis of the wheel is coincident with the z-axis of symmetry of the spacecraft.