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 = 23.5 kg · m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is 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 115 rad/s. If the orientation of the spacecraft is to be changed by 38.0°, for what time interval should the gyroscope be operated?

Explanation / Answer

Ig =23.5 kg.m^2, Is =5*10^5 kg.m^2

from conservation of anglar momentum Isws= Igwg

5*10^5*ws = 23.5*115

ws =5.405*10^-3 rad/s

theta = 38 degrees = 38*2*3.14/360 = 0.663 rad

theta = wt

t = 0.663/(5*405*10^-3) = 122.64 s

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