Coordinate Systems in Physics
Choosing a coordinate system is just choosing how to name a position, and every relation on this page is the arithmetic that moves a point or a vector from one naming scheme to another. The blocks cover the plane in polar form, the two three-dimensional schemes Physics leans on most, the distance and midpoint relations that follow straight from the coordinates, and the component and unit-vector machinery that turns a magnitude and a direction into something an equation can use.
Cartesian coordinates from polar coordinates
Given
- (m)
- (rad)
Distance from the origin from Cartesian coordinates
Given
- (m)
- (m)
Angle from the origin from Cartesian coordinates
Given
- (m)
- (m)
Cartesian coordinates from cylindrical coordinates
Given
- (m)
- (rad)
- (m)
Cylindrical coordinates from Cartesian coordinates
Given
- (m)
- (m)
Cartesian coordinates from spherical coordinates
Given
- (m)
- (rad)
- (rad)
Distance from the origin in space
Given
- (m)
Polar angle down from the z axis
Given
- (m)
- (m)
Azimuthal angle in space
Given
- (m)
Distance between two points in a plane
Given
- (m)
- (m)
Distance between two points in space
Given
- (m)
- (m)
Midpoint of two points in a plane
Given
- (m)
- (m)
A vector in a plane written from its components
Given
- (in the unit of $A$)
- (in the unit of $A$)
A vector in space written from its components
Given
- (in the unit of $A$)
Magnitude of a vector in a plane from its components
Given
- (in the unit of $A$)
- (in the unit of $A$)
Magnitude of a vector in space from its components
Given
- (in the unit of $A$)
Direction of a vector in a plane from its components
Given
- (in the unit of $A$)
- (in the unit of $A$)
Components of a vector from its magnitude and direction
Given
- (in the unit of $A$)
- (rad)
Unit vector along a given vector
Given
A unit vector in a plane written from its direction
Given
- (rad)