In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) 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.

One revolution is equal to 2π radians, hence

$\backslash omega\; =\; \{\{2\; \backslash pi\}\; \backslash over\; T\}\; =\; \{2\; \backslash pi\; f\}\; =\; v\; /\; r$

where ω is the angular frequency or angular speed (measured in radians per second), T is the period (measured in seconds), f is the frequency (measured in hertz), v is the tangential velocity of a point about the axis of rotation (measured in metres per second), and r is the radius of rotation (measured in metres).

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 $\backslash pi$. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics.

For example:

$$

a = - \omega^2 x\;

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

$$

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

Another often encountered expression when dealing with small oscillations is:

$$

\omega^{2} = \frac{k}{m}

where $k$ is the spring constant and $m$ is the mass of the object.

See also

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• Frequency
• Angular velocity
• Radian
• Pulsation

Physical quantity | Angle

Úhlová frekvence | Vinkelfrekvens | Kreisfrequenz | Velocidad angular | Vitesse angulaire | Velocità angolare | Frekuensi angular | Hoeksnelheid | Pulsacja | kotna hitrost | Kulmataajuus | Tần số góc