In physics, **angular frequency** * "ω"* (also referred to by the terms

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

*ω*is the angular frequency (measured in radians per second),*T*is the period (measured in seconds),*f*is the ordinary frequency (measured in hertz) (sometimes symbolised with*ν*).

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 is used to help avoid the confusion^{[3]} that arises when dealing with frequency or the Planck constant because the units of angular measure (cycle or radian) are omitted in SI.^{[4]}^{[5]}

In digital signal processing, the angular frequency may be normalized by the sampling rate, yielding the normalized frequency.

Main article: Circular motion |

In a rotating or orbiting object, there is a relation between distance from the axis, , tangential speed, , and the angular frequency of the rotation. During one period, , 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:

Part of a series on |

Classical mechanics |
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An object attached to a spring can oscillate. 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^{[6]}

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 *ω*_{0}).

As the object oscillates, its acceleration can be calculated by

whereUsing "ordinary" revolutions-per-second frequency, this equation would be

The resonant angular frequency in a series LC circuit equals the square root of the reciprocal of the product of the capacitance (*C* measured in farads) and the inductance of the circuit (*L*, with SI unit henry):^{[7]}

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.

Angular frequency is often loosely referred to as frequency, although in a strict sense these two quantities differ by a factor of 2π.