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This and this articles mention that the angular frequency is:

number of oscillations per unit of time

But this doesn't seem to be correct since the angular frequency is the speed of wave rotation, and Wiki actually says about the wave frequency. Is this correct or I simply don't understand something?

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Yes, you are right. There is an implicit factor of $2\pi$. – Qmechanic♦ Feb 16 '12 at 9:38
Okay, thanks, corrected the article. – ctapobep Feb 16 '12 at 9:55

1 Answer

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If something does a complete rotation per second, everyone agrees it has an angular frequency of 2π radians per second. It is well-known that one complete oscillation is equal to the angle of 2π radians, so the article as written isn't necessarily wrong as 1 oscillation per second is equivalent to 2π radians per second (just different units). However, it could possibly be clearer:

Angular frequency specifies the rate of angular change and is equal in value to 2π radians times the number of oscillations per unit of time.

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Yap, that's the problem with such articles - if you're a beginner and you're not strong in these terms, then uncertainties make things even worse. Like it is in my case. – ctapobep Feb 16 '12 at 22:02

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