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# What Is Angular Velocity?

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• Written By: Andrew Kirmayer
• Edited By: Shereen Skola
• Last Modified Date: 17 September 2019
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2003-2019
Conjecture Corporation
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Angular velocity is often used to describe the rotation of an object in a circular path. It usually defines the rate of change, in relation to time, of angular displacement, or the change in position of a particle or other object. Typically determined by a line perpendicular to the curve of a circle, angular velocity is also perpendicular to the direction in which something is rotating. It is usually calculated by a mathematical formula and can be indicated by the Greek symbol omega.

The speed of an object is generally determined by its angular velocity. To calculate this attribute, the initial position of an object is usually subtracted from the ending position. The number calculated is then divided by the time to get from one place to another. Angular velocity, therefore, is typically measured as travel along a circle in a specific time period. Degrees, revolutions, or units of a circle called radians traveled each second can be calculated; the measurement is also called rotational velocity.

Constant angular velocity can be measured, or an average speed along a path can be determined. Multiplying the average velocity by time can determine the angular displacement, both of which are also components of rotation. The rate at which velocity changes is defined by its acceleration. There are different formulas for calculating each characteristic; some knowledge of Greek letters and symbols, as well as trigonometry, is typically helpful in understanding how to use most of the proper equations.

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The motion of microscopic particles is often determined by calculated angular velocity. Rotation can be positive or negative, depending on the particleâ€™s orientation to the horizontal X axis and the vertical Y axis. Speed is also determined by the point of origin and how the coordinate axes are set up. The movement of a particle, for example, can be assumed to occur around a curve or in a straight line. Angular velocity can be measured in two dimensions; the direction of an object is not specified in this case, while magnitude and direction are both defined for something that is rotating in a three dimensional space.

For an object moving in a path that is not circular, angular linear velocity typically occurs at a right angle to some pre-determined direction. This reference for a position, called a vector, and the velocity of the object generally form an angle that is used in an equation. Two directions of motion can be factored into the calculation. An additional vector, however, can be added to a three-dimensional coordinate system to calculate angular velocity.

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