In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).

It can also be formulated as ω = dθ/dt, the instantaneous rate of change of the angular displacement, θ, with respect to time, t.[2][3] In SI units, angular frequency is normally presented in the unit radian per second.

This convention is used to help avoid the confusion[4] that arises when dealing with quantities such as frequency and angular quantities because the units of measure (such as cycle or radian) are considered to be one and hence may be omitted when expressing quantities in terms of SI units.

[5][6] In digital signal processing, the frequency may be normalized by the sampling rate, yielding the normalized frequency.

In a rotating or orbiting object, there is a relation between distance from the axis,

, a body in circular motion travels a distance

This distance is also equal to the circumference of the path traced out by the body,

Setting these two quantities equal, and recalling the link between period and angular frequency we obtain:

If the spring is assumed to be ideal and massless with no damping, then the motion is simple and harmonic with an angular frequency given by[7]

where ω is referred to as the natural angular frequency (sometimes be denoted as ω0).

The resonant angular frequency in a series LC circuit equals the square root of the reciprocal of the product of the capacitance (C, with SI unit farad) and the inductance of the circuit (L, with SI unit henry):[8]

Adding series resistance (for example, due to the resistance of the wire in a coil) does not change the resonant frequency of the series LC circuit.

For a parallel tuned circuit, the above equation is often a useful approximation, but the resonant frequency does depend on the losses of parallel elements.