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A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 19.5 kgm2 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 = 19.5 kg·m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around 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 to an angular speed of 145 rad/s. If the orientation of the spacecraft is to be changed by 30.0°, for what time interval should the gyroscope be operated?

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