Angular frequency

Angular frequency is a measure of how fast an object is rotating

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 <math>\pi<math>. 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>

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

<math>

Angular frequency

See also