The sagging effect and angular speed.

1. The problem statement, all variables and given/known data

Does any one know anything about the sagging effect of a object with mass m rotating in a circular path at an anle of "theta" below the horrizontal?
How do you find the theoretical angular speed the the object is rotating at R revs/d in t seconds at an angle of "theta" degrees (because of sagging effect caused by gravity). You are given the angular speed in revs/s, the time in t seconds and the force of gravity acting on the object during it's motion but not the angle below the horrizontal. How do you find it.
I'd also like to know how the sagging effect affects the theoretical angular speed.
I would like to know how to find the rea

2. Relevant equations

3. The attempt at a solution
As the object travels downward the potential energy it had is converted to velocity. This is why the object will speed up at the bottom and slow down at the top.

Basically you take the change in height of the object, figure out how much potential energy was converted to kinetic energy over that height and then convert that velocity from m/s to rad/s.

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