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Homework Help: Rotational Kinetic Energy

  1. Nov 14, 2004 #1
    Please, help with rotating rigid body problem

    I am kind of stuck with this problem. Any takers?

    A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal surface with the outside end of the paper nailed to the surface. The roll is given a slight shove (V initial = 0) and commences to unroll. Assume the roll has a uniform density and that mechanical energy is conserved in the process. Determine the speed of the center of mass of the roll when its radius has diminished to r = 1.0 mm, assuming R = 6.0 meters.

    This is what I got so far.

    KE=(1/2)I(Omega)^2

    for the cylinder I is :(1/2)MR^2

    So mgh=(1/2)I(Omega)^2+(1/2)mv^2

    I plugged in I

    mgh=(1/2)(1/2)MR^2(Omega)^2+(1/2)mv^2

    Then I used (omega)=v/r to get here

    mgh=(1/4)MR^2(v/r)^2+(1/2)mv^2 the masses cancel

    gh=(1/4)R^2(v/r)^2+(1/2)v^2

    Now what? How do I get h? Thank you in advance!!
     
    Last edited: Nov 14, 2004
  2. jcsd
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