physics - 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 $\vec{\omega}$ 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

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

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 $π$ . 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' frequency, this equation would be:

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

Angular frequency

See also