(physics) For any oscillation, the number of vibrations per unit time, multiplied by 2π. Also known as angular velocity; radian frequency.
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector
is sometimes used as a synonym for the vector quantity angular velocity.[1]
One revolution is equal to 2π radians, hence[1][2]

where
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In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. From the perspective of dimensional analysis, the unit Hertz (Hz) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω. This convention helps avoid confusion.[3]
In digital signal processing, the angular frequency may be normalized by the sampling rate, yielding the normalized frequency.
For example

where x is displacement from an equilibrium position.
Using 'ordinary' revolutions-per-second frequency, this equation would be

Another often encountered expression when dealing with small oscillations or where damping is negligible is:[4]

where
This is referred to as the natural frequency (which can sometimes be denoted as ω0).
The resonant angular frequency in an LC circuit equals the square root of the inverse of capacitance (C measured in farads), times the inductance of the circuit (L in henrys).[5]

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