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Where do I go wrong?

  1. Sep 12, 2015 #1
    1. The problem statement, all variables and given/known data

    media%2F890%2F890b7412-fcc3-45cd-b501-78515bdfd670%2FphpjjwQAY.png


    3. The attempt at a solution

    A) for disk,


    let w is the angular speed of the disk at the lowest point.

    moment of Inertia of disk about pivot, P = 0.5*M*R^2 + M*R^2

    = 1.5*M*R^2

    Apply conservation of energy

    initial potentila energy = finalkinetic energy


    m*g*R = (1/2)*I*w^2

    m*g*R = (1/2)*1.5*m*R^2*w^2

    m*g*R = (1/2)*1.5*m*(R^2*w^2)

    g*R = (1/2)*1.5*v_disk^2

    2*g*R = 1.5*v_disk^2

    v_disk = sqrt(2*g*R)/sqrt(1.5)

    = 0.816*sqrt(2*g*R)

    = 0.816*v <<<<<<------Answer (wrong! and i don't know why)


    B) for hoop,

    let w is the angular speed of the hoop at the lowest point.

    moment of Inertia of hoop about pivot, P = M*R^2 + M*R^2

    = 2*M*R^2

    Apply conservation of energy

    initial potentila energy = finalkinetic energy


    m*g*R = (1/2)*I*w^2

    m*g*R = (1/2)*2*m*R^2*w^2

    m*g*R = (1/2)*2*m*(R^2*w^2)

    g*R = (1/2)*2*v_hoop^2

    2*g*R = 2*v_hoop^2

    v_hoop = sqrt(2*g*R)/sqrt(2)

    = 0.707*sqrt(2*g*R)

    = 0.707*v <<<<<<------Answer ( wrong and i don't know why)
     
  2. jcsd
  3. Sep 12, 2015 #2

    andrewkirk

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    In both the disk and the hoop problem, when you convert angular velocity to linear velocity of the lowest point, you use R as the radius. What is the distance from the lowest point to the axis of rotation?
     
  4. Sep 12, 2015 #3
    Thanks!!I got it!!
     
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