What is the minimum velocity needed to maintain circular motion at point A?

[fluidistic]

Homework Statement

An inextensible spring with a longitud $$L$$ has a body attached on one of its side (at point $$Z$$ in my figure). The other side of the spring remains fixed (at the center of the circular motion).
The body experiment the gravitational force since the circle is in a vertical plane.
Calculate the minimal velocity (or speed?) when at point $$A$$ that must have the body in order to not be deviated from its circular motion.

Homework Equations

The Attempt at a Solution

I've thought a lot about the problem, but I'm really lost. I know the formulas to encounter the velocity and all this but I don't know how to apply them in this example. I know that if the velocity at point A is 0 then the body will fall vertically. If the velocity is very little then the body will describe a parabola and be deviated from its circular motion... And if he has the velocity I must find, it will remains on its circular motion. I find the problem very interesting but I'm at a loss! I need to be started, like "what happens when the body is at point $$A$$ and its velocity is the one you are looking for?", because I just don't know.

 

[michalll]

Thats easy just take into account centrifugal acceleration.

 

[fluidistic]

I got lucky today, I could ask a professor about

I need to be started, like "what happens when the body is at point A and its velocity is the one you are looking for?"

, he told me that the tension must equals $$0$$.