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  $\vec{\omega}$  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

\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' frequency, this equation would be:

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

Angular Frequency

See also