Imagine an object, moving in a circle.
In a circle there are 2π 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 analagous 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
