A spacecraft is in empty space. It carries on board a gyroscopewith a moment of inertia of Ig = 18.5 kg·m2 aboutthe axis of the gyroscope. The moment of inertia of the spacecraftaround the same axis is 5.00 105 kg·m2.Neither the spacecraft nor the gyroscope is originally rotating.The gyroscope can be powered up in a negligible period of time toan angular speed of 125 rad/s. If theorientation of the spacecraft is to be changed by 30.0°, for what time interval should the gyroscope be operated?