1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Conservation of Energy and Moment of Inertia

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data

    (Q) You hang a thin hoop with Radius R over a nail at the rim of the hoop. You displace it to the side through an angle B (Beta) from its equilibrium position and let it go. What is its angular speed when it returns through its equilibrium position?

    2. Relevant equations

    Change in Potential energy = Mghcm where hcm is the distance moved by the center of mass.

    Rotational Kinetic Energy = 1/2 (IW^2) where W is the angular speed.

    3. The attempt at a solution

    The distance upward moved by the center of mass = R-RCosB.

    Thus, change in potential energy = MgR(1-CosB).

    This should be equal to the rotational Kinetic energy which is 1/2(IW^2).

    Since this is a hoop(not sure what that means), I = MR^2 (Hope I am correct!!)

    Thus, MgR(1-CosB) = 1/2 (MR^2)(W^2)
    Thus, W = sqrt [(2g/R)(1-CosB)].

    Unfortunately, according to my book, the 2 isn't supposed to be there. Can someone please help me figure out why this is so? Thank-you very much!!
  2. jcsd
  3. Oct 13, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

  4. Oct 13, 2007 #3
    Thanks a ton! That was really a wake-up call. I can't believe how careless I've been. Thanks again!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook