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# Angular frequency

This article has been reviewed by the following Topic Editor: Peter Saundry

Angular frequency is the repetition rate of a cyclic process measured in radians/sec.

 Animation showing the relationship between angular frequency (radians per second) and frequency (cycles per second). Angular frequency is larger by a factor of 2π. Source: Wikipedia An angle of 1 radian results in an arc with a length equal to the radius of the circle. Source: Wikipedia. A complete revolution is 2π radians (shown here with a circle of radius one and circumference 2π). Source: John Reid, Ufo karadagli, Wikipedia

A radian is the ratio between the length of an arc and its radius. A complete revolution is 2π radians (i.e. the arc of a full circle is its circumeference; 2π times the radius) .

Thus, an object rotating one full cycle per second has an angular frequency of 2π radians/sec. Or, more generally, if the frequency in cycles/sec is f (v in the animation right), then the angular frequency ω = 2πf.

## Citation

Steve Baum (Lead Author);Wikipedia (Content Source);Peter Saundry (Topic Editor) "Angular frequency". In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth March 8, 2010; Last revised Date October 8, 2011; Retrieved May 18, 2013 <http://www.eoearth.org/article/Angular_frequency>

## The Author

Assistant Research Scientist, Physical Section Department of Oceanography Texas A&M University   ... (Full Bio)