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Spinning satellites

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I have the following problem:

A zero-momentum spinner has a momentum wheel spinning at 5000 rpm. The angular momentum of the wheel is 100 N-m-s.

a) What is the spin rate of the spacecraft if its moment of inertia, Is = 500 kg-m2?
b) What is the moment of inertia of the wheel?
c) If the wheel suddenly stops, what would the spin rate of the satellite be?
d) Assuming the wheel was fixed, how long would it take to get the wheel back up to a speed of 4000 rpm applying a motor torque of 0.1 N-m?
e) What would the new spin rate of the spacecraft be?

Please show all work. Thank you for your help.

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It was given in the problem that,

For the wheel
the angular momentum of the wheel (L) = 100 Js &
the angular velocity of the wheel (w)= 5000 rpm = 5000 X 2(pi)/60 ( since 1 rpm = [2(pi) / 60] rad/s )

For the Space craft, Moment of inertia (Is) = 500 Kg-m^2

a) to calculate the spin rate, we need to apply the Law of conservation of angular momentum between the space craft and the wheel. According to this,

(I1)(w1) = (I2)(w2) = L ( Let 1 corresponds ...

Solution Summary

This solution provides step by step calculations for spin rate and moment of inertia.