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Unit vector in polar coorindate

  1. Sep 15, 2011 #1
    In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1

    However, how about in polar coorindate?
    3r+1[itex]\theta[/itex] (r and [itex]\theta[/itex] are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.)

    Dose it mean a line with lenght 3 from origin and angle 1 radian from x-axis?
     
  2. jcsd
  3. Sep 16, 2011 #2

    Hootenanny

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    Yes, just as 3i+j means three "steps" in the x-direction and 1 "step" in the y-direction, 3r + 1[itex]\theta[/itex] means three "steps" away from the origin and 1 "step" counter-clockwise from the x-axis.
     
  4. Sep 16, 2011 #3
    How to convert the vector in retangular corrdinate to polar coordinate?
    For example, 3i+j, how to write in polar corrdinate unit vector?
     
  5. Sep 16, 2011 #4

    Hootenanny

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    For a detailed explanation see here: http://en.wikipedia.org/wiki/Polar_coordinate_system

    In polar coordinates, the radius is simply the distance from the origin (i.e. the magnitude of your position vector). So in your example, [itex]r = |3\hat{i} + \hat{j}| = \sqrt{10}[/itex]. The angular component is simply the angle between your vector and the positive x-direction. Since your point is in the first quadrant, this is simply [itex]\theta=\arctan(y/x) = \arctan(1/3)[/itex]. If your point were to be in a different quadrant, you would have to adjust accordingly.
     
  6. Sep 16, 2011 #5
    I am still very unfamiliar with this new topic, and I still have a lot of question marks in my head.

    The details of my reply please refer to my attachment
     

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  7. Sep 16, 2011 #6

    Hootenanny

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    The unit vector [itex]\vex{e}_\theta[/itex] represents an "additional" rotation from the vector [itex]\vec{e}_r[/itex]. Notice that the unit vector [itex]\vec{e}_r[/itex] is the direction from the origin to the point in space [itex]\vec{r}[/itex]: http://en.wikipedia.org/wiki/File:Polar_unit_vectors.PNG.
     
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