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Rotational problem

  1. Dec 12, 2006 #1
    I'm kinda stuck in this mechanical problem, ill try to describe the situation.

    A plane, homogeneous disk may slide on a frictionless horizontal table. A cord is fastened to the disc and wrapped many times around the rim of the disc. The cord goes without friction through a small eyelet at the edge of the table and is connected to a mass m. The mass of the disc is M and its radius is R. The system is started from rest and the cord is assumed to be taut throughout the motion. Ignore the mass of the cord.

    http://ylle.eu/DSC00602.JPG (my sketch of the problem)

    Describe the velocity of the disc as a function of time.

    Here is what i have computed of equations so far.

    The forces affecting the disc M must be M(d²x)/(dt²) = mg
    The forces affecting the mass m must be m(d²x)/(dt²) = mg - S

    The torque(N) exerted on M can be described as

    N = mgR

    The moment of inertia for a circular disk around its CM is

    I = (1/2)MR²

    The angular momentum is

    L = Iw

    Torque equals the change of angular momentum with respect to time

    N = Iw'
    N = (1/2)MR²w'
    mgR = (1/2)MR²w'

    And from this point i cant really seem to maky any more observations that can help me solve the problem.
    I hope someone can clarify the problem for me

    Thanks in advance
    Mikkel
     
  2. jcsd
  3. Dec 12, 2006 #2

    OlderDan

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    Science Advisor
    Homework Helper

    You need to rethink the force acting on the disk. Look at what you did for the hanging mass and think about the connection between the two objects.
     
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