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.