Angular frequency

Imagine an object, moving in a circle.

In a circle there are 2&pi radians. A radian is a measurement of angle, and is more convenient than the degree when doing calculations.

If the object completes one circle in T seconds, then the angular frequency, ω, is given by

ω = 2π/T

ω has units s^-1.

Using angular frequency in the equations is often a convenient shorthand, as it hides π symbols.

As circular motion viewed 'edge on' is analogous to simple harmonic motion, ω will often appear in the equations of SHM.

For example:

a = -ω² x

Using 'ordinary' frequency, this equation would be a lot uglier:

a= - 4π²f² x

ω is related to 'ordinary' frequency by the equation:

ω=2πf

This is easily seen, as

f=1/T