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Cylindrical and Spherical Coordinates Changing

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Convert the following as indicated:

    1. r = 3, θ = -π/6, φ = -1 to cylindrical

    2. r = 3, θ = -π/6, φ = -1 to cartesian

    3. The attempt at a solution
    I just want to check if my answers are correct.

    1. (2.52, -π/6, 1.62)
    2. (-2.18, -1.26, 1.62)
     
  2. jcsd
  3. Sep 9, 2012 #2

    LCKurtz

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    What coordinate system are these given in? ##r## is usually used in cylindrical coordinates and ##\rho## for spherical. Also, if ##\phi## is the spherical coordinate angle from the ##z## axis, it is usually restricted to the interval ##[0,\pi]##. Are you sure you copied the ##\phi## values correctly?
     
  4. Sep 9, 2012 #3

    vela

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    Mathematicians and physicists use ##\theta## and ##\phi## differently. You need to tell us which convention you're using here.
     
  5. Sep 9, 2012 #4
    Here is the question with the answer key:
    cIwN3.png

    In this case r = ρ and I'm not sure why phi is negative.

    I don't think the answer key is correct.
     
  6. Sep 9, 2012 #5

    vela

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    The answer key is correct. You need to show us your calculations. To answer #1, it's probably most straightforward if you do #2 first and the convert from Cartesian to cylindrical.
     
  7. Sep 9, 2012 #6
    For number one, how can r be negative? They have -2.52 whereas I have 2.52. It is why I thought the answer key was wrong.
     
  8. Sep 9, 2012 #7

    vela

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    When r is negative, you reflect through the origin from where you'd otherwise be. In polar coordinates, for instance, the point r=-1, θ=π/4 would correspond to (-1/√2, -1/√2), which is where you'd end up if you reflected r=1, θ=π/4 through (0,0).

    You'll notice they gave you a second answer where r is positive, but the angle has been changed to account for the reflection.
     
  9. Sep 11, 2012 #8
    Lastly, when ρ is negative does that mean the angle starts from the -z axis? Because when ρ is positive it starts from the positive z axis.
     
  10. Sep 11, 2012 #9

    vela

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    Not exactly. Reflection in spherical coordinates takes ##\phi \to \pi-\phi## and ##\theta \to \theta+\pi##. The change to ##\phi## effectively means you're measuring from the -z-axis, but you also have to accompany it with a rotation by 180 degrees about the z-axis.
     
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