Physics-Need help with centripetal acceleration problem ASAP?

[Matt W]

Here is the problem
"A small bead can slide without friction on a circular hoop that is in a vertivcal plane. The fact that the hoop is fictionless means that the hoop exerts a normal force that points toward the center of the hoop. The hopp exerts no force other than that on this bead. The hoop has a radius of (0.10m)

If the hoop rotates at an angular speed= 24 rad/s, find the angle theta at which the bead is in vertical equilibrium? and then find What happens if the angular speed is 6 rad/s?

I started with a free body diagram with mg force downward, the normal force facing the center of the circle(hoop). So therefore the force vertical is (Forcenormal) x (sin (theta)). And parallel is (Forcenormal) x (cos(theta)).

key Fn=normal force
f=ma
so Fn(sin theta)= mass x gravity
solved for M= (Fn(sin theta)) / g

Fn(cos theta)=m A(centripetal)
plugged M into this equation
i got Fn(cos theta) / Fn(sin theta)*gravity=ac
which simplifies to (cot theta x 9.8)=ac
so then i found the acceleration by the equation ac= (v^2)/ R

ac= (24 rad/s)^2 / (0.10)
then i plugged this into the equation

cot theta= 9.8 * ( 24)^2/ 0.10

im stuck there am i on the right track, i need help finishing it