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 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:
Using 'ordinary' frequency, this equation would be a lot uglier:
ω is related to 'ordinary' frequency by the equation:
This is easily seen, as
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