The formula for centrifugal force can be written as mw^2r or mv^2/r, how do I figure if centrifugal force is direct or inverse proportional to the radius?

Question

The formula for centrifugal force can be written as mw^2r or mv^2/r,  how do I figure if centrifugal force is direct or inverse proportional to the radius?

anonymous · Answer

First you have to write centrifugal force in terms of radius:$$F _{c}=\frac{ mv ^{2} }{ r }$$If centrifugal force varies directly with radius, then centrifugal force would increase as radius increases.  If Fc varies inversely, it will decrease as radius increases or it will increase as radius decreases.

anonymous · Answer

So, what happens to Fc as r gets really big?

anonymous · Answer

I do know what is direct or inverse, what I dont get is, two versions of the same formula has the radius^-1, which one do I use to figure the proportion?

anonymous · Answer

That depends on whether angular velocity or tangential velocity is constant. If angular velocity is constant, then you use:
$$F _{c}=\omega ^{2}r$$.  If neither is specifically stated as being constant, then you'll have to describe how Fc varies with radius when ω is constant and how it varies with radius when v is constant.

anonymous · Answer

Alright, thanks for your time.