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I Torque and precession

  1. Nov 16, 2016 #1

    Physics Dad

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    Gold Member

    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 1.92×104 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 1.20×10-6 degree during a 5.00 hour exposure of a galaxy?

    Equations
    I=mr2
    L=Iω
    Ω=dΦ/dt
    τ=ΩL

    Variables and Conversions
    m=2.00kg
    r=0.025m
    dΦ=(1.20×10-6×2π)/360 = 2.09×10-8 rad
    dt=5×60×60=1800s
    ω=(1.92×104×2π)/60 = 640π rad/s

    Attempt at Solution

    I=(2.00kg)(0.025)2=1.25×10-3kgm2
    L=(1.25×10-3kgm2)(640π)=4π/5
    Ω=(2.09×10-8)/(1800)=1.16×10-12

    τ=(1.16×10-12)(4π/5)

    =2.92×10-12Nm

    My answer is incorrect. Any help would be greatly appreciated. This is the ridiculous "mastering physics" website. It is the most pointless thing ever. I would much rather we were given an assignment to complete as at least then you can receive constructive feedback as opposed to simply being told the answer is wrong.

    I am happy to be wrong as long as I can understand why. I am sure I have just made a simple mistake, like use the wrong equation or miscalculate something, but with no guidance I can't fix it.

    Thank you.
     
  2. jcsd
  3. Nov 16, 2016 #2

    Charles Link

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    Homework Helper

    It looks almost completely correct to me, but I found one arithmetic mistake: ## \Omega =1.16 E-11 ##. (You missed the exponent by one unit). At least I think that's one place that needs a correction.... editing..that would make the answer 2.92 E-11 if everything else is correct, which I think it may be.
     
    Last edited: Nov 16, 2016
  4. Nov 16, 2016 #3
    Well, I'm not sure if you can call it helpful, but I don't see anything wrong with this. I am 99.9% sure this is the right approach, and I checked almost all of the math. (I could only approximate multiplying by pi in the last step. doing it in my head while lying in bed.)
     
  5. Nov 16, 2016 #4
    I suck. What hurts more than having said I didn't see anything wrong is saying so AFTER you already found this mistake. Jeez.
     
  6. Nov 16, 2016 #5

    Charles Link

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    That tends to re-enforce my belief that this might be the OP's only error. Looking forward to hearing from the OP.
     
  7. Nov 17, 2016 #6

    Physics Dad

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    Thank you all for the replies, turns out there was a mistake in the system and my answer of 2.92*1012 was correct after all. Had this verified by 3 lecturers at uni today.

    You can all sleep easy now.

    Thanks again.
     
  8. Nov 17, 2016 #7

    Charles Link

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    Very good, except when you said you had the correct answer after all, I was pretty sure there must be a second error and I found it: ## dt=(5)(60)(60)=18000 ##, instead of 1800. Glad you got the right answer, but looks like you had offsetting errors.
     
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