# 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 [itex]\vec{\omega}[itex] 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

[itex]\omega = {{2 \pi} \over T} = {2 \pi f} = v / r[itex]

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

For example:

[itex]

a = - \omega^2 x\; [itex]

Using 'ordinary' frequency, this equation would be:

[itex]
a = - 4  \pi^2  f^2  x\;


[itex]

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