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Rotational Motion of a Hanging Mass

  1. Nov 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider a ball of mass m on the end of a string of length l. It hangs from a frictionless pivot. The ball is pulled out so that the string makes an angle thetai with the vertical and is then released.
    a. Find w (angular velocity) as a function of the angle the strings makes with the vertical. (Hint: Use conservation of energy.)
    b. Find the angular momentum of the ball using |L| = ml^2w
    c. Show that t = dL/dt by differentiating L and finding t from its definition.

    2. Relevant equations
    U1 + K1 = U2 + K2
    V = rw

    3. The attempt at a solution
    for a:

    The answer, according to the book, is w = sqrt(2g/l*(cos(theta) - cos(thetai)))

    I used the conservation of energy and got w = sqrt(2g/l*(1 - cos(thetai))). I'm lost.. I don't know where the book got cos(theta)
  2. jcsd
  3. Nov 20, 2009 #2


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    Homework Helper

    at an angle θi, find the energy at that point.

    Now this energy is converted into gravitational pe and ke at an angle θ. Find this energy here.

    Equate the two.
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