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

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Angular velocity (ω) is defined as ω = 2πf, where f represents frequency in revolutions per second. This equation illustrates the relationship between frequency and angular velocity, with frequency indicating the number of complete cycles in a given time period. The factor of 2π arises because one complete revolution corresponds to 2π radians. Therefore, while frequency is measured in cycles, angular velocity is measured in radians per second. Understanding this relationship is crucial for grasping the concepts related to the period of sinusoidal motion in simple harmonic motion (SHM).
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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.
 
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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
 
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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.
 

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