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

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

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:

Using 'ordinary' frequency, this equation would be:

See also

• Frequency
• Angular velocity
• Radian
• Pulsation