The Hubble Space Telescope is stabilized to within an angle of about 2 millionth

Question

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 2.00 kg and diameter 5.00 cm , spinning about its central axis.

How large a torque would it take to cause these gyroscopes to precess through an angle of 1.10×106 degree during a 5.50 hour exposure of a galaxy in N*m?

Explanation / Answer

Torque = dL/dT

= /t

I =mr2

gyroscope torque is rate of change of momentum

Torque =[ ( angular momentum before – angular momentum after ) / 5.5x 60x60 ]

Torque, T = (Ibefore – Iafter)/ 19800

Plug in the values

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