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Rod+mass rotating clockwise

  1. Jan 28, 2017 #1
    1. The problem statement, all variables and given/known data
    The 3.0 kg rod has a length of 80 cm. The 4.0 kg rectangle attached to the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal.

    https://gyazo.com/9d0bb4ce2fed98b192f173a918549f60

    ^image


    2. Relevant equations
    mgh = potential energy
    ( w^2 * i ) * .5 = rotational energy
    i = moment of inertia
    moment of intertia for rod rotated on end = (m * L^2) * .333
    L = length
    m = mass
    w = angular speed
    THE ANSWER SHOULD BE 5.19 rad/s

    3. The attempt at a solution
    *For the height, I found the center of gravity which is .63 meters, i think the length stays .8 though
    mgh = (w^2 * i ) * .5
    mgh = (w^2) * (m * L^2) * .333 * .5
    7 * 10 * .63 = ( w^2 ) * (7 * .8 * .8 ) * .333 * .5
    44.1 = (w^2) * .746
    59.115 = (w^2)
    7.68 = w
    7.68 rad/s ????????
     
  2. jcsd
  3. Jan 28, 2017 #2
    Being the genius I am, I have self-analyzed my own work and found my error. For the rotational energy. I must find the rotational energy of the mass first, then the rod:
    ( ( w^2 ) * .5 * 4 * .8 * .8 ) and ( ( w^2 ) (3* .8 * .8 ) / 3 ) then add them and take out the w ^ 2 since the angular acceleration should be equal for both:
    ( w^2 ) ( (.5 * 4 * .8 * .8 ) + ( ( 3 * .8 * .8 ) /3 ) )
    I was however correct to have found the center of gravity for mgh.
     
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