Understanding Angular Velocity: W = 2pi(f) ?

[mlostrac]

Can anyone explain to me how angular velocity (w) = 2pi(f) -->where f = frequency.

This is not a homework question involving numbers. I'm reading a section on "the period of sinusoidal Nature of SHM" and I don't understand how they get this equation.

 

[irycio]

frequency-number of rotations in a period of time, usually one s
w-angular velocity-angle in an amount of time
2pi-one full circle
hence w=2pif

 

[Redbelly98]

In case the previous explanation was not quite clear: f and ω use different units to express the frequency. f expresses the frequency in terms of revolutions or number of complete cycles, while ω uses radians. 1 revolution is 2π radians (or 360 degrees), hence the factor of 2π in the relation between f and ω.