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Kinematics of Rigid Bodies in 3D

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Problem 15.18:
    J9f4r.jpg

    I've defined the positive J (fixed) axis along the pole pointing upwards and the positive X (fixed) axis going to the right, with both centered at the point of contact between the hoop and the pole, which I will refer to as point O. The rotating axes (lower case) are defined along the fixed axes at this particular moment.


    2. Relevant equations
    ω=Ω(J) + v/R(k) = Ω(j) + v/R(k)
    α=(Ωv)/R(i) <-- derived from the first expression of ω
    VA = VO + ω x rA/O + VA/O = v(j) - 2ΩR(k)
    aA = aO + α x rA/O + ω x (ω x rA/O) + aA/O = (-2Ω2R-2v2/R)(i)


    3. The attempt at a solution

    My issue is that my v2/R term in my final acceleration is off by a factor of 2. I get -240 ft/s2(i) when I should be getting -216 ft/s2(i). Can anyone point me towards the step that I multiplied by 2 when I shouldn't have?
     
  2. jcsd
  3. Apr 5, 2012 #2
    Actually I found the problem, I left off the 2ω x VA/O term in the acceleration formula. That adds in another V2/R term that solves my factor of 2.
     
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