A satellite in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope is Ig = 21.5 kg⋅m2 about the axis of the gyroscope, and the moment of inertia of the rest of the satellite is Is = 5.00×105 kg⋅m2 about the same axis. Initially both the satellite and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 105 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the satellite's orientation by 34.0∘ ? s
