Bead on a vertical ring centripetal acceleration

[keshavm01]

Homework Statement

There is a vertical ring with a bead strung on it. The vertical ring spins at 4 revolutions per second, and the the bead moves up the ring at what angle from the bottom of the ring will the bead be at equilibrium? Is it possible for the bead to make it all the way up to the same elevation as the center of the ring? What will happen if the ring only spins at one revolution per second? The ring itself has a radius of 0.100 m and the bead has no friction with the ring.

Homework Equations

radial acceleration= v^2/R = 4(pi)^2*R/(T)^2
v=velocity
R=radius
T=time of revolution

The Attempt at a Solution

I tried to use the acceleration equations above to calculate the radial acceleration of the bead, but that doesn't explain why or how much the bead moves up the ring?

 

[SammyS]

Draw a free body diagram for the bead.