A spaceship in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope isIg = 24.5 kg · m2about the axis of the gyroscope, and the moment of inertia of the rest of the spaceship isIs = 5.00 ✕ 105 kg · m2about the same axis. Initially both the spaceship and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 120 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the spaceship's orientation by 40.0°?
