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Homework Help: Crane Problem, Finding Angular Velocity

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data

    At the instant shown in the figure , the crane's boom has an angle = 33.0 and rotates around the vertical axis with angular velocity = 8.00×10^−2 radians/s that increases at the rate = 7.00×10^−2 radians/s^2. At the same instant, the crane's boom is rotating upward with angular velocity = 3.00×10^−2 that increases at the rate = 5.00×10^−2 . Determine wx, wy, and wz, the i, j, and k components of w, the boom's angular velocity in the fixed reference frame X, Y, Z. The translating-rotating reference frame, x, y, z, lines up with the fixed reference frame at the instant shown.

    > The figure shows a crane with the z-axis vertical and the y-axis along the cranes boom. The angular velocity are all rotating counterclockwise. The origin is at the center of the crane.

    2. Relevant equations

    vp = wp X rp

    vp is the velocity at a point
    w is the angular velocity
    rp is the position of the vector at a point

    3. The attempt at a solution

    w = w1 * w2 = (.03i + .08k)rad/s
    [tex]\Omega[/tex] = .08k rad/s
    w = [tex]w_{12}[/tex] + [tex]\Omega[/tex] X w = (.05i + .07k) + .08k X (.03i + .08k)

    =0.05i + 0.0024j + 0.07k

    That was my final answer but it is wrong.
     
  2. jcsd
  3. Jul 22, 2010 #2
    How are you taking the acceleration of the crane into account?
     
  4. Jul 22, 2010 #3
    I'm taking into account the acceleration in my equation but the answer is still not correct:

    w = + [tex]\Omega[/tex] X w = (.05i + .07k) + .08k X (.03i + .08k)
     
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