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Rotation: disk and pulley

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data

    A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley and mass m is suspended from the other end. Assume that the disk drops vertically.

    a. relate the accelerations of mass m and disk ,a and A, respectively to the angular acceleration of the disk.

    b. Find a, A and α.

    2. Relevant equations



    3. The attempt at a solution

    equations of motion : T - mg = ma
    T - Mg = MA

    -TR = [itex]\frac{1}{2}[/itex]MR[itex]^{2}[/itex]α

    Are these equations of motion wrong????
     
  2. jcsd
  3. Nov 23, 2013 #2

    haruspex

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    Which direction are you taking as positive, up or down? If up, I would write that as ma = T + mg etc., where g takes a negative value. But it's maybe a matter of personal preference.
    They look ok to me, but you've not written out the relationships between A, a, α and R. That is where this question fools some people.
     
  4. Nov 24, 2013 #3
    I took up as the positive direction. But I think T and g are always opposing each other. I have written a constraint equation A + a = Rα. But the clue given in the book is " if A= 2a then α= 3A/R"
     
  5. Nov 24, 2013 #4
    That's a typo in the book. There was a thread on the same problem recently.
     
  6. Nov 24, 2013 #5

    haruspex

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    The consensus is that it's an error in the book. It should say α= 3a/R. See https://www.physicsforums.com/showthread.php?t=722327
     
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