# Cylindrical coordinates question

• theBEAST
In summary: So in the Cartesian frame, the line defined by theta = 0 in the cylindrical frame points along the y-axis of the Cartesian frame.

## Homework Statement

https://dl.dropbox.com/u/64325990/cylindrical.PNG [Broken]

## The Attempt at a Solution

Okay so I found r = 2.24 and z = -3. However I am stuck at finding theta. I think I just don't understand what the question means when it says "In addition, the line defined by theta = 0 in the cylindrical frame points along the y-axis of the Cartesian frame.". I think it means that the new theta = 0 is the y-axis. If that is the case then theta would be greater than 180°/3.14rads. This is obviously wrong; could anyone please explain what is meant by this question?

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compute theta for the standard cyl coords and then subtract pi/4. in xyz a line in the y direction would have a theta of pi/4 but in the problems it should have 0.

the problem is describing a another cyl coord system different from the one conventionally used to get you to think about what you're doing and what it means to translate points from xyz to another coord system.

jedishrfu said:
compute theta for the standard cyl coords and then subtract pi/4. in xyz a line in the y direction would have a theta of pi/4 but in the problems it should have 0.

the problem is describing a another cyl coord system different from the one conventionally used to get you to think about what you're doing and what it means to translate points from xyz to another coord system.

Okay so I found that the theta for the standard cylindrical coordinates is 5.176. Then if I subtract is by pi/4 I get 4.391. I am still lost :S Don't you mean subtract pi/2? But even then the answer is wrong.

theBEAST said:
Okay so I found that the theta for the standard cylindrical coordinates is 5.176. Then if I subtract is by pi/4 I get 4.391. I am still lost :S Don't you mean subtract pi/2? But even then the answer is wrong.
If θ is measured counter-clockwise in the cylindrical system, then it will be measured clockwise in the Cartesian system.

## 1. What are cylindrical coordinates?

Cylindrical coordinates are a type of coordinate system used to locate points in three-dimensional space. It consists of a radial distance (r), an angle in the xy-plane (θ), and a height above the xy-plane (z).

## 2. How do you convert from Cartesian coordinates to cylindrical coordinates?

To convert from Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z), you can use the following equations:
r = √(x² + y²)
θ = tan⁻¹(y/x)
z = z

## 3. What is the difference between cylindrical and spherical coordinates?

The main difference between cylindrical and spherical coordinates is the inclusion of an additional angle in spherical coordinates. While cylindrical coordinates use two angles (θ and φ), spherical coordinates use three angles (θ, φ, and ρ) to locate a point in three-dimensional space.

## 4. How are cylindrical coordinates used in physics and engineering?

Cylindrical coordinates are commonly used in physics and engineering to describe the location of objects in cylindrical or rotational systems. They are particularly useful for problems involving circular motion, such as in fluid dynamics, electromagnetism, and structural engineering.

## 5. Are there any limitations or disadvantages to using cylindrical coordinates?

One limitation of cylindrical coordinates is that they are not suitable for describing points that lie at the origin (r = 0). Additionally, they can be more complex to use and visualize compared to Cartesian coordinates, which may make them less intuitive for some applications.