Rotating a mass horizontally to raise a mass vertically

[Ocata]

Homework Statement

Hi,

Suppose a mass attached to a massless string is being swung in a horizontal circle with uniform circular motion, and on the other end of the string is hanging vertically with a mass attached to it. If the mass in uniform circular motion is swung around fast enough, it could pull on the string in a way that the mass attached to the other end will start to move upward such that the vertical portion of the string decreases and the horizontal portion of the string increases (that is, the radius of the uniform circular motion is increases).

So if I wanted to know the speed of the mass or the rate that the vertical mass is increasing and things like this, how could I do so?

Is there a specific description or name to this type of problem that I could research to learn more about it?

I heard someone describe this but can't find anything in my physics book within the chapter on Newton's Laws.

Can this type of scenario be solved with uniform circular motion properties and F=ma?

I haven't learned about Work and Kinetic Energy yet, so hopefully that is not necessary for describing this type of problem.

Thanks

Homework Equations

Don't know which equations yet as I can't find anything on it yet.

The Attempt at a Solution

No attempt yet. Looking first to find where a problem of this type exists.

 

[haruspex]

I assume the circulating mass is on a smooth table (though you could also consider the case where it hangs down at an angle).
This is not a specific topic. Just analyse each part of the system in terms of the (variable) tension in the string. The hanging mass simply obeys T-mg=ma, while the circulating mass has a more complex behaviour. For that, look up acceleration in polar coordinates.