Angular frequency

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 <math>\vec{\omega}<math> is sometimes used as a synoym 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

<math>

\omega = {{2 \pi} \over {T}} = {2 \pi f} = v / r <math>

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)

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

For example:

<math>

a = - \omega^2 x\; <math>

Using 'ordinary' frequency, this equation would be:

<math>

<math>

See also

• Frequency
• Angular velocity
• Radian
• Pulsation