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String wrapped around hoop

  1. Mar 1, 2014 #1
    1. The problem statement, all variables and given/known data
    A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass 0.180kg. The free end of the string is held in place and the hoop is released from rest. After the hoop has descended 60.0cm , calculate the angular speed of the rotating hoop and the speed of its center.


    2. Relevant equations
    K=Iω2
    U = mgh
    ω=v/r
    I = 1/2 mr2

    3. The attempt at a solution
    Ei = mgh = (0.180)(9.8)(0.6) = 1.0584
    Ef = 1/2 mv2+1/2 Iω2 = 3/4(0.08)2ω2
    Ei = Ef
    I got ω = 14.9 rad/s (I've also tried 35 rad/s) Is my math wrong or something?

    For the second part, I saw somewhere the equation was v=√gh and but I was thinking I could just use ω=v/r but since I didn't have ω I couldn't solve that one.
     
  2. jcsd
  3. Mar 1, 2014 #2

    TSny

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    Gold Member

    Hello, PKay.

    Is this the correct formula for a hoop?
     
  4. Mar 1, 2014 #3
    I think so. The problem is the axis is in the middle for that equation but since it's on the side, I'm not too sure anymore.
     
  5. Mar 1, 2014 #4

    TSny

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