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

inertia of the spacecraft around the same axis is /= 5.00 x 105 kgm2. 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 100rad/s. If the orientation of the spacecraft is to be changed by 30.0 degrees, for what time interval should the gyroscope be operated?