Spacecraft Is In Empty Space

A . 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 X 105 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 100 sπ1. If the orientation of the spacecraft is to be changed by 30.0°, for how long should the gyroscope be operated?

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