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Rotation Problem/Total Kinetic Energy

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data
    A spool of mass 8.67kg and radius 4.58m is unwound by a constant force 48.1N pulling on the massless rope wrapped around it. Assume the moment of inertia of the spool about O is 3/4mr^2 and it rolls w/o slipping. When the center of the spool has moved a distance d, find the total kinetic energy (In terms of F and d).

    2. Relevant equations
    Work= ke(final)- ke(initial)

    3. The attempt at a solution
    I'm feeling pretty lost, but I was thinking that if I just added the rotational energy + translational kinetic energy that that would give me the answer. Obviously it is not this easy and I have no idea how to put it in terms of force and distance.
  2. jcsd
  3. Dec 2, 2008 #2
    The most I can get is as follows, the angular velocity, as the force of the massless string is exerted on the circumference of the spool,


    From the definition, [tex]\tau=I\cdot\alpha[/tex],
    [tex]\tau=\dfrac{3}{4}mr^{2}\times5.55=757\;Nm = Fr[/tex]

    Also note that from the definition of Nm, 757 Nm = 757 Joules.

    Kinetic energy is,
    [tex]F\cdot d=\dfrac{1}{2}mv^2[/tex]

    The circumference of the wheel is [tex]2\pi r[/tex], this needs to be factored into Fr to relate the rotation angle to the ultimate displacement of the center, O?

    Hope you can make some progress from this...
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