Centrifugal force versus gravity (ball on a joint placed on rotating shaft)

[LachieD]

Homework Statement

Basically, this is the problem.

[PLAIN]http://img180.imageshack.us/img180/3598/physicsproblem.png

It's related to some design research I'm doing regarding a centrifugal control valve. This is a type of valve that controls the fluid flow based on the centrifugal force that effects the weigths strapped onto the valve shaft. The higher rpm (the shaft is connected to a small turbine powered by the fluid flow), the higher centrifugal force, and the higher the ball should raise (in actual case, connected with the valve disc, but let's ignore that in this ideal case). Now, I'm trying to calculate the neccesary rpm value for a desired angle of the joint holding the ball from vertical line. Ideal system.

Homework Equations

Did I setup the problem correctly? Can this be observed as a static problem as I did? What am I doing wrong? I see if the angle increases toward the value of 90, the neccesary rpm goes into infinity. Is this normal?

Thank you.

The Attempt at a Solution

My attempt is included in the picture.

 

[nvn]

LachieD: If the input units for n are Hz, post 1 currently looks correct.

 

[LachieD]

Yeah, that is correct. Thanks. I was just wondering if the problem was setup correctly.