The angular frequency is a quantity resulting from the rotational motion of a vector and is used in the calculation of frequency-dependent impedances and reactances. The angular frequency is designated by the Greek letter small omega 'omega'.
In order to be independent of the radius of the circle in the case of a rotational motion as represented by a sinusoidal signal, one does not specify the circumferential velocity but the velocity of the rotating vector. Instead of specifying the angle, which is 360 degrees for a full circle, one uses the radian of `2pi`, where `pi` is a Greek letter and has a value of 3.14159265.... has. This value is obtained from the ratio of the circumference of the circle to the diameter of the circle.
If the vector with radius 1 rotates once per second, then the distance traveled is 360 degrees or `2pi`. The distance traveled is therefore proportional to the frequency of the rotating vector.