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Velocity vector and velocity intensity

  1. Dec 7, 2016 #1
    1. The problem statement, all variables and given/known data
    Given the velocity vector in the polar coordinates, ##\vec v=-awsin{wt}\vec e_r + awcos{wt}\vec e_\theta## determine the average velocity vector and velocity intensity over a time period ##[0, \pi/2w]##
    2. Relevant equations
    3. The attempt at a solution

    For the first part where the average velocity vector is to be found i use
    ##\vec v_{avg}=\frac{\int_{0}^{\pi/2w}\vec vdt}{\pi/2w}##
    and for the intensity part i use
    ##v=\sqrt{v^2_r+v^2_\theta}## first find the intensity which is just ##v=aw## and since the intensity is equal at all times i get for the second part
    ##\frac{2aw}{\pi/2w}## but i dont get correct results, where is my mistake?
     
  2. jcsd
  3. Dec 7, 2016 #2

    haruspex

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    Which resulted in ....?
    right.
    Think again about that step.
     
  4. Dec 8, 2016 #3
    Well.. isnt average acceleration then just ##(v_i+v_f)/2##? Shouldnt i just get ##aw## then?
     
  5. Dec 8, 2016 #4

    haruspex

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    Yes. No need to divide by the period.
     
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