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Circular Motion Kinematics

  1. May 16, 2016 #1
    1. The problem statement, all variables and given/known data
    The rod OA rotates clockwise with a constant angular velocity of 6 rad/s. Two pin-connected slider blocks located at B move freely on OA and the curved rod whose shape is a limacon described by the equation r = 200*(2-cosθ) mm. Determine the magnitude of the acceleration of the slider blocks at the instant θ = 135°.
    QcsaAag.jpg
    2. Relevant equations
    αr=r''-rθ'2
    αθ=rθ''+2r'θ'
    α = √(αr2θ2)

    3. The attempt at a solution
    I am trying to solve for the magnitude using the normal and tangential acceleration components.
    r = 200*(2-cosθ) --> r(135) = 541.42 mm θ' = 6 rad/s
    r' = 200 sinθ * θ' --> r'(135) = 848.53 mm/s θ'' = 0
    r'' = 200cosθ * θ'2= -5091.17 mm/s2

    When I plug all those values in I keep getting the wrong answer. Can someone tell me where I am going wrong?
     
  2. jcsd
  3. May 16, 2016 #2

    TSny

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    Gold Member

    Careful with the signs. Note that the rod is rotating clockwise.
     
  4. May 16, 2016 #3
    Can you explain that more? Is this because there is a negative change in θ over time?
     
  5. May 16, 2016 #4
    I ended up getting the right answer, must have just been a miscalculation.
     
  6. May 16, 2016 #5

    TSny

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    Yes. In the figure, ##\theta## increases in the counterclockwise direction. Therefore, if the rod rotates clockwise, ##\dot{\theta}## is a negative number. You should find that ##\dot{r}## is negative when ##\theta = 135^o##.
     
  7. May 16, 2016 #6
    Okay I understand that. Thank you for explaining. I just go lucky in my calculations because they ended up cancelling the negatives out.
     
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