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Rotational dynamics Find acceleration

  1. Oct 25, 2014 #1
    • Posting problems as images is against forum guidelines and generatr less response
    1. The problem statement, all variables and given/known data
    http://imgur.com/eYoa8Ut

    2. Relevant equations
    Torque=rt=I(alpha)
    t-mg=-ma
    alpha = a/r

    3. The attempt at a solution
    t-mg=-ma is the equation for the hanging mass.
    To find how much this turns the small wheel,
    rt=I(alpha) I and r are known
    rt=Ia/r

    I'm not sure what to do from here. If I try and solve for a and t now, it gives an incorrect answer. I think this is due to me not doing anything with the larger wheel yet, but I'm not sure what to do with it. I know that the tension in the upper and lower part of the belt are not equal, and both produce torque of their own. Tupper should produce a clockwise moment, Tlower should produce a counterclockwise moment.
     
    Last edited: Oct 25, 2014
  2. jcsd
  3. Oct 26, 2014 #2

    haruspex

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    Quite so. So include these in your torque equation for the smaller wheel and write down the torque equation for the larger wheel.
     
  4. Oct 26, 2014 #3
    So for the smaller wheel:
    tr+(Tl)R-(Tu)R=I(alpha)
    Larger wheel gives:
    (Tu)(Rlw)-(Tl)(Rlw)=I(alpha)

    So now I have 2 equations and four unknowns. t,(Tl),(Tu),(alpha)
    I can write t=mg-ma and alpha as a/r, Does alpha = a/r for the small wheel use the smaller or larger radius? Since its a tangential I would assume the larger.
    That gives
    (mg-ma)r+(Tl)R-(Tu)R=Ia/R
    and
    (Tu)(Rlw)-(Tl)(Rlw)=Ia/(Rlw)

    If this is right I'm now down to 3 unknowns and only 2 equations.
     
  5. Oct 26, 2014 #4

    haruspex

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    Look carefully at how Tu and Tl appear in these equations. Notice anything?
     
  6. Oct 26, 2014 #5
    I see, multiplied equation 1 by R(lw) and equation 2 by R and added them. Then Tu and Tl cancel and you can solve for a. Got the right answer Thanks.
     
  7. Oct 26, 2014 #6

    haruspex

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    Good.
    Note what this means physically. Suppose the belt is elastic. Making it tighter will increase both tensions equally, but won't affect the answer to the question.
     
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