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 I_g = 19.0 kg middot m^2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is 5.00 times 10s kg-m^2. 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 150 rad/s. If the orientation of the spacecraft is to be changed by 30.0 degree, for how long should the gyroscope be operated? s

Explanation / Answer

By Conservation of angular momentum

I1W1=I2W2

19*150=(5*105)*[(30*pi/180)/t]

t=91.86 s

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