| Angular frequency | |
|---|---|
 | |
Other names | angular speed, angular rate |
Common symbols | ω |
| SI unit | radian per second (rad/s) |
Other units | degrees per second (°/s) |
| InSI base units | s−1 |
Derivations from other quantities | ω = 2πrad⋅ν,ω = dθ/dt |
| Dimension | |
Inphysics,angular frequency (symbolω), also calledangular speed andangular rate, is ascalar measure of theanglerate (the angle per unit time) or thetemporal rate of change of thephaseargument of asinusoidal waveform orsine function (for example, in oscillations and waves).Angular frequency (or angular speed) is the magnitude of thepseudovector quantityangular velocity.[1]
Angular frequency can be obtained by multiplyingrotational frequency,ν (or ordinaryfrequency,f) by a fullturn (2πradians):ω = 2π rad⋅ν.It can also be formulated asω = dθ/dt, theinstantaneous rate of change of theangular displacement,θ, with respect to time, t.[2][3]
InSIunits, angular frequency is normally presented in the unitradian persecond. The unithertz (Hz) is dimensionally equivalent, but by convention it is only used for frequency f, never for angular frequency ω. 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]
Indigital signal processing, the frequency may be normalized by thesampling rate, yielding thenormalized frequency.
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: Circular motion on the unit circle is given bywhere:
| Part of a series on |
| Classical mechanics |
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Core topics |
An object attached to a spring canoscillate. If the spring is assumed to be ideal and massless with no damping, then the motion issimple and harmonic with an angular frequency given by[7]where
ω is referred to as the natural angular frequency (sometimes be denoted asω0).
As the object oscillates, its acceleration can be calculated bywherex is displacement from an equilibrium position.
Using standard frequencyf, this equation would be
The resonant angular frequency in a seriesLC circuit equals the square root of thereciprocal of the product of thecapacitance (C, with SI unitfarad) and theinductance of the circuit (L, with SI unithenry):[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.
Although angular frequency is often loosely referred to as frequency, it differs from frequency by a factor of 2π, which potentially leads confusion when the distinction is not made clear.
angular frequency.
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