Angular frequency

Angular frequency ω (in radians per second), is larger than frequency ν (in cycles per second, also called Hz), by a factor of 2π. This figure uses the symbol ν, rather than f to denote frequency.

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is 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 angular velocity. The term angular frequency vector \vec{\omega} is sometimes used as a synonym for the vector quantity angular velocity.^[1]

One revolution is equal to 2π radians, hence^[1][2]

\omega = ,

where

k is the spring constant

m is the mass of the object.

ω is referred to as the natural frequency (which can sometimes be denoted as ω₀).

As the object oscillates, its acceleration can be calculated by

a = - \omega^2 x \; ,

where x is displacement from an equilibrium position.

Using 'ordinary' revolutions-per-second frequency, this equation would be

a = - 4 \pi^2 f^2 x\; .

LC circuits

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]

\omega = \sqrt{1 \over LC}

See also

• Orders of magnitude (angular velocity)
• Simple harmonic motion
• mean motion

References and notes

• Olenick ,, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe. New York City: Cambridge University Press. pp. 383–385, 391–395.