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Rolling ball down slope at specific time

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    A uniform solid ball rolls down a slope. If the ball has a diameter of .5m and a mass of .1 kg find the following:

    The equation which describes the velocity of the ball at any time, given that it starts from rest.


    2. Relevant equations

    I've tried using energy equations, thus: 1/2 Iw^2+1/2Mv^2+mgh = constant (Kf +Uf = Ki + Ui) but that doesn't have "t" as a variable. I have also tried θ-θi=1/2(ωi+ω)t. But that didn't end up taking the radius or mass into consideration.

    3. The attempt at a solution

    More or less stated in the relevant equations. This is due in a few hours, so anything is much appreciated. Thank you in advance!
     
  2. jcsd
  3. Nov 3, 2011 #2

    rl.bhat

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    Homework Helper

    Moment of inertia of the sphere is 2MR^2/5 and v = R*w.
    So the rotational kinetic energy is given by 1/2*I*w^2 = 1/2*2M*R^2/5*v^2/R^2 = M*v^2/5.
    And h = 1/2*g*sin(theta)*t^2.
    Substitute these values in the relevant equation to solve for t.
     
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