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 = 19.0 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 125 rad/s. If the orientation of the spacecraft is to be changed by 30.0°, for what time interval should the gyroscope be operated?
s

Explanation / Answer

Using conservation of angular momentum L

L gyroscope =L space craft   or
L1 =L 2
L = I

=t=30.0° =/6

2 =(I1/I2)1

/6=2t=
t =/6/[(I1/I2) 1]
t=(/6)/[(19.0/5.00x105) 125] = 63 s

This is assuming instant speed on and instant stop. Inreality the gyroscope would accelerate the spacecraft to that speedand then stop by reversing the angular momentum. If no otherforces involved t on = t stop . During ton and t stop the spacecraft willmove under angular acceleration and - respectively.

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