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Homework Help: Please, still need help with rotating rigid body problem

  1. Nov 15, 2004 #1
    :cry: I am still stuck with this problem. Please, help if you can.
    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.


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

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

    I plugged in I


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

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


    Now what? How do I get h? Did I miss anything? Thank you in advance!!
  2. jcsd
  3. Nov 15, 2004 #2


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    Dearly Missed

    1. At the start, the total system has only potential energy, MgR, where M is the total mass of the paper.
    2. At time "t", you should find that the mass of the remaining rolled-up paper, m, is:
    3. The potential energy of the total system remaining at time "t" is:
    4. The kinetic energy of the total system at time "t" is:
    by using the rolling condition to relate the angular velocity to the center of mass of the rolled up paper.
    5. Hence, you get:
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