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]}
In SI units, angular frequency is measured in radians per second, with units s^{−1} since radians are unitless.
One revolution is equal to 2π radians, hence^{[1]}^{[2]}
where
Angular frequency is therefore a simple multiple of ordinary frequency. However, using angular frequency is often preferable in many applications, as it avoids the excessive appearance of π. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.
For example:
Using 'ordinary' revolutionspersecond frequency, this equation would be:
Another often encountered expression when dealing with small oscillations or where damping is negligible is:^{[3]}
where
This is referred to as the natural frequency.
Angular frequency inside an LC circuit can also be defined as the square root of the inverse of capacitance (measured in farads), times the inductance of the circuit (in henrys).^{[4]}
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In physics (specifically mechanics and electrical engineering), angular frequency ω (also referred to by the terms angular speed, radial frequency, and radian frequency) is a scalar measure of rotation rate.
Angular frequency is the magnitude of the vector quantity angular velocity. The term angular frequency vector $\backslash vec\{\backslash omega\}$ is sometimes used as a synonym for the vector quantity angular velocity .
In SI units, angular frequency is measured in radians per second, with dimensions t^{−1} since radians are dimensionless.
