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Cylindrical and Spherical Coordinates Changing

  • Thread starter theBEAST
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  • #1
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Homework Statement


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

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)
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


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

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)
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?
 
  • #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.
 
  • #4
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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.
 
  • #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.
 
  • #6
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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.
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.
 
  • #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.
 
  • #8
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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.
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.
 
  • #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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