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Ax and Ay As a linear combination of Atan and Arad

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is about a rod that is set in a pendulum way but that has an angle high enough so the SHM doesn't apply to it. It starts at Pi/2 until it reachs 0. I was able to find the tangential and radial acceleration about the center of mass but now I need to know the x and y acceleration about the center of mass.


    2. Relevant equations

    It says that I should be using the angle between Atan and Ax as a reference

    3. The attempt at a solution

    Completly stuck!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 10, 2012 #2

    tiny-tim

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    welcome to pf!

    hi spirof! welcome to pf! :smile:
    the only difficulty is working out the angle between tan (or rad) and x (or y) …

    the hint is simply telling you to write those angles as either ±θ or ±(90° - θ) …

    go for it! :wink:
     
  4. Mar 10, 2012 #3
    Re: welcome to pf!

    Thanks u did put me on the track, I do possess all the θ already for a definite period of time. Actually, correct if I am wrong, if I have and angle of 1.40 rad, then if if i do pi/2 - 1.4, which will give me something around 0.17 rad.

    From there, i know that the angle between arad and ax is 0.17 rad, the same angle betweenay and atan. I would then be tempted to simply do ax = ar cos 0.17. However, I cannot assume that they form a right angle triangle. Anymore inputs?
     
  5. Mar 10, 2012 #4

    tiny-tim

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    hi spirof! :smile:
    i'm confused :redface: … there's right-angles everywhere …

    which angle isn't a right- angle? :confused:
     
  6. Mar 10, 2012 #5
    Well between Ar and Ax, If u look at my attached image, you will see that I cannot assume that they are parts of a right angle triangle. Ax seems to long to be the hypothenus of Ar, doesn't it?
     
  7. Mar 10, 2012 #6

    tiny-tim

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    the length doesn't matter

    all you need is the angle between ar and ax
     
  8. Mar 10, 2012 #7
    Thanks, I went over the internet and I have found the solution. I have to express as linear combination of the Ar and Atan.

    It sums up to Ax = Ar cos (90-θ) + Atan sin (90-θ)
    Ay = -Ar sin (90-θ) + Atan cos (90-θ)
     
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