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## 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 1.92×10^4 rpm. Although the structure of these gyroscopes is actually quite complex, we can model each of the gyroscopes as a thin-walled cylinder of mass 2.00kg and diameter 5.00cm , 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 degrees during a 5.00 hour exposure of a galaxy?

## Homework Equations

Torque = [itex]\frac{dL}{dt}[/itex] (1) , Ω = [itex]\frac{Δ∅}{Δt}[/itex] (2)

## The Attempt at a Solution

For a gyroscope torque is a a rate of change of momentum (1). So,

Torque = [itex]\frac{Angular momentum before - Angular momentum after}{5X60X60}[/itex]

Torque = [itex]\frac{I(ωbefore) - I(ωafter)}{18000}[/itex]

This reduces down to Torque = [itex]\frac{∏}{90000}[/itex] - [itex]\frac{ωafter}{800X18000}[/itex]

I am at a loss of how to find ω after, could anyone shed some light? Cheers

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