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 $F_c$ 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!