Angular frequency (ω) (Physics Dictionary)

Angular frequency (ω)

Also angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance.

A scalar measure of rotation rate. It refers to the angular displacement per unit time (e.g. in rotation) or the rate of change of the phase of a sinusoidal waveform (e.g. in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the vector quantity that is angular velocity. The term angular frequency vector ω → {\displaystyle {\vec {\omega }}} is sometimes used as a synonym for the vector quantity angular velocity.^[13] One revolution is equal to 2π radians, hence^[13][14]

ω = 2 π T = 2 π f , {\displaystyle \omega ={{2\pi } \over T}={2\pi f},}

where:

ω is the angular frequency or angular speed (measured in radians per second),

T is the period (measured in seconds),

f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν).