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Find the aceleration of the disk when falling (rotation)

  1. Jun 29, 2012 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=48751&stc=1&d=1341000426.gif

    I have that system and the problem says:

    A disk of mass M and radious R are posed are shown. The disk is hanging by an ideal rope which is coiled up. From a smooth axis through the center of the disk is haning a body m. Calclate the module of the aceleration of the center of mass of the disk.

    2. Relevant equations



    3. The attempt at a solution

    I've done this excercise but without the small mass hanging there. What I did was to use the torque and newton formulas, that simple. But here I've got two bodies and tensions are driving me crazy. Should I consider the bodies as a single one?

    Thanks!
     

    Attached Files:

  2. jcsd
  3. Jun 29, 2012 #2

    tiny-tim

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    Hi Hernaner28! :smile:
    Yes, since they're moving together, you can regard them as a single body …

    add the m to the mass of the pulley, but not to its moment of inertia. :wink:
     
  4. Jun 29, 2012 #3
    Done! Thank you!!

    attachment.php?attachmentid=48753&stc=1&d=1341006280.gif
     

    Attached Files:

  5. Jun 29, 2012 #4

    tiny-tim

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    yes! :smile:

    here's a shortcut (i don't know whether your professor would approve of this, but it's certainly a good way of checking the answer) …

    the force is (M+m)g, and the effective mass is the actual mass M+m plus the "rolling mass" I/r2 = M/2,

    so a = (M + m)/(3M/2 + m) :wink:
     
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