A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 20.0 kg m2 about the axis of the gyroscope.

A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 20.0 kg · m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is = 5.00 10^5 kg · m2. Neither the spacecraft nor the gyroscope is originally rotating. The gyroscope can be powered up in a negligible period of time to an angular speed of 120 rad/s. If the orientation of the spacecraft is to be changed by 30.0°, for what time interval should the gyroscope be operated?