The rotor of an electric motor has rotational inertia Im = 8.14 times 10-3 kg-m2

Question

The rotor of an electric motor has rotational inertia Im = 8.14 times 10-3 kg-m2 about its central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe; the probe has rotational inertia Ip = 7.52 kg-m2 about this axis. Calculate the number of revolutions of the rotor required to turn the probe through 17.5 degree about its central axis. Number Units rev The number of significant digits is set to 3; the tolerance is +/-2%

Explanation / Answer

Im=8.14*10-3 kg-m2

Ip=7.52 kg-m2

using conservation of angular momentum

Imwm = Ipwp => Im(dm/dt) = Ip(dp/dt) cancelling dt on both sides and putting dp = 17.50 = 7pi/72 gives

dm=(Ip/Im)(7pi/72) giving dm = 89.82 pi = 44.91 revolutions

answer=44.91 units rev

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