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Mastering Physics: Rotational Motion Around Two Cylinders

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data

    The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of the cylinders? Assume that the cylinders turn on a frictionless axle. I know the answer is 3.5 rad/s2.

    Figure: http://session.masteringphysics.com/problemAsset/1176936/5/P7-59.jpg


    2. Relevant equations

    [itex]\alpha[/itex]=τ/I
    τ=rF
    I=1/2*M*R2

    3. The attempt at a solution

    I tried calculating the net torque of the cylinders caused by the hanging masses. I then divided the net torque by the total inertia on the cylinders using the first equation listed above.
     
  2. jcsd
  3. Mar 4, 2013 #2

    SammyS

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    What is the total moment of inertia of the combined cylinders?
     
  4. Mar 5, 2013 #3
    They don't give it to you in the problem. Would I calculate the inertia on each disk and add those together to get the total inertia of the disk system?
     
  5. Mar 5, 2013 #4

    SammyS

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    Yes. That's how I would do it.
     
  6. Mar 5, 2013 #5
    But once you find the inertia what would you do from there?
     
  7. Mar 5, 2013 #6

    SammyS

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    Well, earlier you mentioned calculating the net torque.

    How is the acceleration of each mass related to the angular acceleration of the compound cylinder?
     
  8. Mar 5, 2013 #7

    haruspex

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    That overlooks the inertia of the two hanging masses. Safest is to assign a tension variable to each rope, an angular acceleration variable for the cylinders, and write out three free body equations.
     
  9. Mar 5, 2013 #8
    I think it may be easier to post my work than trying to explain it. This is what I have done, and I am unsure where my error may be. Any help is greatly appreciated!
     

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  10. Mar 5, 2013 #9

    SammyS

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    Easier, but very hard to read.

    The acceleration is not the same for both blocks.
     
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