The space station is initially not rotating. Its reaction control system exerts a constant couple on it until it has rotated 90◦ , then exerts a constant couple of the same magnitude in the opposite direction so that its angular velocity has decreased to zero when it has undergone a total rotation of 180° . The maneuver takes 6 hours. The station’s moment of inertia about the axis of rotation is I = 1.5 × 10 ¹⁰ kg-m ² . How much work is done in performing this maneuver? In other words, how much energy had to be expended in the form of reaction control fuel?