Stabilization of the Hubble Space Telescope.? 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 19,200 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 2.0 kg and diameter 5.0 cm, spinning about its central axis. How large a torque would it take to cause these gyroscopes to precess through an angle of 1.0 X 10-6 degree during a 5.0-hour exposure of a galaxy?
Solution 56E Introduction From the given angular displacement and time we can calculate the angular speed of precession. Then using the formula of angular speed of precession we can calculate the required torque. Step 1 The angular displacement is = 1.0 × 10 ° = 1.745 × 1rad The time is t = 5.0 hr = 18000 s Hence the angular speed of precession is Step 2 The moment of inertia of the gyroscope about the spinning axis is We know that the mass of the gyroscope is m = 2.00 kg and the radius of the gyroscope is r = (2.0 cm)/2 = 1.0 cm = 1.0 × 10m So the moment of inertia is