Radial coordinate

Definition

A radial coordinate is a measure of distance from a fixed origin point in a polar or spherical coordinate system. It specifies the length along the radius vector from the origin to a given point.

5 Must Know Facts For Your Next Test

1. The radial coordinate is denoted as $r$ in polar coordinates and as $\rho$ in cylindrical coordinates.
2. In polar coordinates, a point is defined by its radial coordinate $r$ and angular coordinate $\theta$.
3. The radial coordinate must be non-negative: $r \geq 0$.
4. In spherical coordinates, the radial coordinate $r$ defines the distance from the origin to the point, with additional angles $\theta$ (azimuthal angle) and $\phi$ (polar angle) specifying direction.
5. Radial coordinates are crucial for problems involving circular or spherical symmetry, simplifying equations of motion and field expressions.

Review Questions

• What does the radial coordinate represent in a polar coordinate system?
• How is a point specified in spherical coordinates using its radial coordinate?
• Why must the radial coordinate be non-negative?

Related terms

Polar Coordinates: A two-dimensional coordinate system where each point is determined by a distance from a reference point (the origin) and an angle from a reference direction.

Spherical Coordinates: A three-dimensional coordinate system that extends polar coordinates with an additional angle, defining points by their distance from the origin and two angles.

Cylindrical Coordinates: $\text{A three-dimensional extension of polar coordinates, specifying points by }(\rho, \phi, z)$, where $\rho$ is the radial distance, $\phi$ is the azimuthal angle, and $z$ is height along the z-axis.