Question

A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of I = 20.5 kg m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is 5.00 x 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 150 rad/s. If the orientation of the spacecraft is to be changed by 27.0°, for what time interval should the gyroscope be operated?

Answer 1

here, we can use conservation of angular momentum

as both spacecraft and gyroscope were originally not moving, we have

I1w1 = I2w2 = 0

we also know that

w = $\theta$ / t ( note that w has units of rad/sec)

so,

w = 27 / t

we need to convert 27 degree to radians ( 1 deg = pi / 180 rad)

w = 0.4712 / t

so,

20.5 * 150 = 5e5 * 0.4712 / t

t = 76.62 sec