A spacecraft is in empty space. It carries on board a gyroscope with a moment of

Question

A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 24.0 kg m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is = 5.00 times 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 140 rad/s. If the orientation of the spacecraft is to be changed by 32.0 degree, for what time interval should the gyroscope be operated? s

Explanation / Answer

by conservation of angulaw momentum Ig*wg = Is*ws putting values gives ws = 6.72*10^-3 rad/s required rotation,a = 32 degrees = 0.5585 rad time for this rotation,t = a/ws = 0.5585/6.72*10^-3 = 83.11 s

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