Let's assume that a particular ring of radius $r$ is spinning at angular speed $\omega$, then a person of mass $m$ in this ring will experience a [centrifugal force][1] $F_c$ given in magnitude by
$$
  F_c = m r\omega^2
$$
and pointing radially outward.  If this person were to apply Newton's second law in this rotating frame and treat this apparent outward force as he would a gravitational force on the surface of the Earth where the force is given in mangitude by $mg$ where $g$ is the acceleration due to gravity, then he would find that
$$
  mg = m r \omega^2
$$
and therefore, he would experience an effective gravitational acceleration which is a function of $r$ and is given by
$$
  \boxed{g_\mathrm{eff} = r\omega^2}
$$
So we see that the effective acceleration due to gravity in a given ring increases linearly with the radius of the ring and quadratically with its angular speed.

I just saw that someone else also wrote and answer that takes it from here, so I hope this helps!

Cheers!

  [1]: http://en.wikipedia.org/wiki/Centrifugal_force