Question

how does angular frequency relate to the frequency, in words and an equation?

Answer 1

Angular frequency is 2*pi*frequency, or:
\[\omega=2\pi f\]
If you think a rotating body, the frequency tells how many times in a second it will rotate around its axis. The angular frequency tells how many radians it rotates in a second.

I love this animation on the page:
http://en.wikipedia.org/wiki/Angular_frequency