# Dynamics/Kinematics/Coordinate Systems/Polar

## Introduction[edit | edit source]

*Content from polar coordinate system*

In mathematics, the **polar coordinate system** is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the *pole*, and the ray from the pole in the reference direction is the *polar axis*. The distance from the pole is called the *radial coordinate*, *radial distance* or simply *radius*, and the angle is called the *angular coordinate*, *polar angle*, or *azimuthj*.^{[1]} The radial coordinate is often denoted by *r* or *ρ*, and the angular coordinate by *φ*, *θ*, or *t*. Angles in polar notation are generally expressed in either degrees or radians (2π rad being equal to 360°).

Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more intuitive to model using polar coordinates.

The polar coordinate system is extended to three dimensions in two ways: the cylindrical and spherical coordinate systems.

## References[edit | edit source]

- ↑ Brown, Richard G. (1997). Andrew M. Gleason. ed.
*Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis*. Evanston, Illinois: McDougal Littell. ISBN 0-395-77114-5. https://archive.org/details/advancedmathemat00rich_0.