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Torque to rotate spinning gyroscope

  1. Dec 2, 2011 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations
    L=I*ω
    torque = Ω*L
    I=mr^2
    Ω=Δθ/Δt


    3. The attempt at a solution
    ω=1.92*10^4rpm
    =2010.62rad/s

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

    Δθ=1.3*10^6deg
    =7.4484*10^-5rad

    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: Dec 2, 2011
  2. jcsd
  3. Dec 3, 2011 #2
    Check this again:
    Δθ=1.3*10^-6deg
    =7.4484*10^-5rad
     
  4. Dec 3, 2011 #3
    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
     
  5. Dec 21, 2011 #4
    I think 1.27*10^-11 is not the correct answer , how is the question being solved in the correct way ?
     
  6. Nov 24, 2012 #5
    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.
    I just had to do the same problem so I decided to answer your question.
     
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