Conversion of cartesian coords to spherical polars

In summary, the problem involves rewriting the velocity vector v in spherical polar coordinates and unit vectors. The formula for r, theta, and phi are given, and the attempt at solving the problem involves rearranging the expression for v and substituting using the given formulae. However, the solution is not yet found, and help is needed.
  • #1
kelbear
1
0

Homework Statement



Velocity vector, v:

v = (yi + xj) / (x^2 + y^2 + z^2)^(3/2)

"Re write "v" in spherical polar coordinates and unit vectors"


Homework Equations



Obviously
r = (x^2 + y^2 + z^2)^(1/2)
theta = tan^(-1)((x^2 + y^2)^(1/2)/z)
phi = tan(^-1)(y/x)

The Attempt at a Solution



Have tried rearranging the expression for v and substituting using the above formulae but not getting anywhere. I know its a simple question but am obviously missing something basic.
Any help is very much appreciated x
 
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  • #2
welcome to pf!

hi kelbear! welcome to pf! :smile:

(have a theta: θ and a phi: φ and a square-root: √ and try using the X2 and X2 icons just above the Reply box :wink:)

"unit vectors" means er and eθ, the unit vectors in the radial and transverse directions

(so for example er = r/r)
 

1. What is the formula for converting cartesian coordinates to spherical polar coordinates?

The formula for converting cartesian coordinates (x, y, z) to spherical polar coordinates (r, θ, φ) is:
r = √(x² + y² + z²)
θ = arccos(z/r)
φ = arctan(y/x)

2. How do I determine the range of values for θ and φ in spherical polar coordinates?

θ ranges from 0 to π (or 0° to 180°) and represents the angle between the positive z-axis and the vector from the origin to the point.
φ ranges from 0 to 2π (or 0° to 360°) and represents the angle between the positive x-axis and the projection of the vector onto the xy-plane.

3. Can negative values be used in spherical polar coordinates?

Yes, negative values can be used in spherical polar coordinates. Negative values for r will result in the point being located in the opposite direction from the origin, while negative values for θ and φ will result in the point being located in the opposite direction from the positive axis.

4. How do I convert spherical polar coordinates to cartesian coordinates?

The formula for converting spherical polar coordinates (r, θ, φ) to cartesian coordinates (x, y, z) is:
x = rsinθcosφ
y = rsinθsinφ
z = rcosθ

5. Can I use spherical polar coordinates to represent points in 3D space?

Yes, spherical polar coordinates can be used to represent points in 3D space. They are particularly useful in describing points that are located at a certain distance and direction from the origin, as well as points that lie on a sphere. However, cartesian coordinates may be more useful for describing points in certain situations, such as when working with rectangular objects or when performing calculations involving distance and direction.

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