# Torque to rotate spinning gyroscope

## Homework Statement

The Hubble Space Telescope is stabilized to within an angle of about 2 millionths of a degree by means of a series of gyroscopes that spin at 1.92×104 . Although the structure of these gyroscopes is actually quite complex, we can model each of the gyroscopes as a thin-walled cylinder of mass 2.00 and diameter 5.00 , spinning about its central axis.
How large a torque would it take to cause these gyroscopes to precess through an angle of 1.30×10−6 degree during a 5.00 hour exposure of a galaxy?

L=I*ω
torque = Ω*L
I=mr^2
Ω=Δθ/Δt

## The Attempt at a Solution

ω=1.92*10^4rpm

I=mr^2
=2(0.005)^2
=0.005

Δθ=1.3*10^6deg

Δt=5 hours
=18000s

torque = Ω*I*ω
=(7.4484*10^-5/18000)*0.005*2010.62
=4.1*10^-8 Nm

This is the wrong answer and I feel as if the torque shold be rather larger by intuition. Any help would be appreciated.

Edit: 3.17*10^-12 Nm turned out to be the correct answer, but i'd still like to know how to do this question.

Last edited:

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Check this again:
Δθ=1.3*10^-6deg

sorry, i made a mistake in my original post, the given angle is 1.3^-6deg.

ok, so now i get
Δθ=2.2*10^-8deg

torque=(2.2*10^-8/18000)*0.005*2010.62
=1.27*10^-11

I think 1.27*10^-11 is not the correct answer , how is the question being solved in the correct way ?

The problem with your solution, in case you are still wondering,
is I= mr^2
not I=md^2
therefore you take the diameter of 5 divide it by 2.
So I=2(0.025^2)
and that would be the last error after the conversion of degrees to radians which you fixed.