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Determine the Velocity and Acceleration of the Rotating Rod

  1. Mar 26, 2013 #1
    1. The problem statement, all variables and given/known data
    The body is formed of slender rod and rotates about a fixed axis through point O with the indicated angular properties. If ω = 4.6 rad/s and α = 4.4 rad/s2, determine the instantaneous velocity and acceleration of point A.

    I have attached an image of the question

    2. Relevant equations

    v = wXr

    a = αXr + wX(wXr)

    3. The attempt at a solution

    r = <0.5sin(24)i + 0.23cos(24)i +0.5cos(24)j - 0.23sin(24)j>

    r = <0.4135i + 0.3632j + 0k>

    w = 4.6k

    va = <0i + 0j + 4.6k> X <0.4135i + 0.3632j + 0k>

    VA = 1.6707i + 1.9021j

    But it says this is wrong. What am I missing?

    I know for the second part that I need to use:

    aA = αXr + wX(wXr) but I can't seem to get wXr right.

    Any advice would be greatly appreciated.

    Attached Files:

  2. jcsd
  3. Mar 26, 2013 #2
    well I see that you are using 0.23m as the distance from the straight part of the rod to the point A. However, I think 0.23m is the radius of the cirular part of the rod, so then the distance you should be using would be the diameter 0.46m.
  4. Mar 26, 2013 #3
    You are correct. Thank you. My final correct answers are:

    V_A = 1.24i + 2.869j

    a_A = -12.01i + 8.449j
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