Angular Frequency of AC voltage

[member 392791]

Hello,

I am wondering, what is the physical interpretation of the angular frequency of AC voltage? I don't see the physicality of what the angle for which there is a frequency?

I understand that the voltage can switch back and forth at a certain rate, which jives in my mind with the idea of frequency: How quickly the voltage switches back and forth in its magnitude. However, I don't understand what the angular frequency represents?

 

[BruceW]

there is going to be terms like cos(f * t * 2PI) where f is frequency and t is time. So it is just easier to write cos(w * t) where w is the angular frequency.