Spherical, Cylindrical Coordinates - quick easy questions

In summary, vector subtraction works the same in spherical and cylindrical coordinates as in cartesian, and the modulus for a vector can be calculated the same way in all three coordinate systems."
  • #1
FrogPad
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EDIT: I figured it out.

I'm sick, tired, and just confusing myself. I have a test in a few hours, and would like to clear some easy stuff up so I'm not thinking about it during the test.

1)
Vector subtraction works in spherical and cylindrical coordinates right?

That is to say, [itex] \vec {AB} [/itex], points from point [itex] A [/itex] to point [itex] B [/itex] where [itex] \vec {AB} = \vec B - \vec A [/itex] in spherical, cylindrical, and cartesian?

For some reason I'm thinking that I read somewhere that we first need to convert to cartesian, but that might actually be related to my second question.

2)
Is the modulus for a vector the same in cartesian, cylindrical, and spherical coordinates? I mean if I am trying to find the length in spherical.
[tex] \vec V_{sph} = (R, \theta, \phi) [/tex]
Isn't [itex] R [/itex] just the length from orgin. It doesn't make sense to say that, [itex] | \vec V_{sph} | = \sqrt{(R)^2+(\theta)^2+(\phi)^2} [/itex].

The same for cylindrical, is [itex] | \vec V_{cyl} | = \sqrt{(r)^2 + (z)^2} [/itex] ?

Thanks!

EDIT: I figured it out
 
Last edited:
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  • #2
.Yes, vector subtraction works the same in spherical and cylindrical coordinates as it does in cartesian.The modulus for a vector can also be calculated the same in all three coordinate systems.For a vector in spherical coordinates, the modulus is given by | \vec V_{sph} | = \sqrt{(R)^2+(\theta)^2+(\phi)^2} , while in cylindrical coordinates it is given by | \vec V_{cyl} | = \sqrt{(r)^2 + (z)^2} .
 

1. What are spherical coordinates?

Spherical coordinates are a type of coordinate system used to specify the position of a point in three-dimensional space. They use two angles, usually denoted as theta (θ) and phi (φ), and a distance from the origin (r) to define the location of a point.

2. How do spherical coordinates differ from Cartesian coordinates?

Spherical coordinates use angles and a distance from the origin to specify a point, while Cartesian coordinates use three distances (x, y, and z) to define a point. Spherical coordinates are often used in situations where the distance from the origin is more relevant than the specific directional components of a point.

3. What are cylindrical coordinates?

Cylindrical coordinates are another type of coordinate system used in three-dimensional space. They use an angle (θ), a distance from the origin (r), and a height (z) to specify the position of a point. Cylindrical coordinates are often used in situations where the height of a point is more relevant than the specific directional components.

4. How are spherical and cylindrical coordinates related?

Spherical and cylindrical coordinates are related through a simple transformation. The distance (r) and angle (θ) in cylindrical coordinates can be converted to spherical coordinates using the following equations:
x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ, where φ is the angle used in spherical coordinates.

5. What are some real-world applications of spherical and cylindrical coordinates?

Spherical coordinates are commonly used in physics and engineering, such as in celestial mechanics to describe the position of planets and satellites. Cylindrical coordinates are often used in areas such as fluid mechanics and electromagnetism, as they are well-suited for describing cylindrical objects and systems. Both coordinate systems are also used in computer graphics and 3D modeling.

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