Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_176

6/176 A space telescope is shown in the figure. One of the reaction wheels of its attitude-control system is spinning as shown at 10 rad/s, and at this speed the friction in the wheel bearing causes an internal moment of \(10^{-6}\) N·m. Both the wheel speed and the friction moment may be considered constant over a time span of several hours. If the mass moment of inertia of the entire spacecraft about the x-axis is \(150(10^3)\) kg·m², determine how much time passes before the line of sight of the initially stationary spacecraft drifts by 1 arc-second, which is 1/3600 degree. All other elements are fixed relative to the spacecraft, and no torquing of the reaction wheel shown is performed to correct the attitude drift. Neglect external torques.