The elements of a spacecraft with axial mass symmetry and a reaction-wheel contr

Question

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 = 3.4 N ·m for a time period t = 36 s, 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 = 197 kg ·m2 and that of the wheel alone is Iw = 12.2 kg ·m2. The spin axis of the wheel is coincident with the z-axis of symmetry of the spacecraft. The angular velocities are positive if in the +z-direction, negative if in the -z-direction.

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