Ring, collar, and roller problem

1. Jul 24, 2008

sdavidmiller

Hey,
It's been about a year since I took mechanics, and I had agreed to help a friend out today. She gave me this problem, and I'm drawing a blank at how to approach it. No solution necessary, just an approach!

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

A thin, uniform ring of mass m and radius R is attached by a frictionless pin to a collar at A and rests against a small roller at B. The ring lies in a vertical plane, and the collar can move freely on a horizontal rod and is acted upon by a horizontal force P. Express the angle THETA between the collar and the vertical axis at equilibrium

EDIT: The image is at http://www.filedropper.com/wheelproblem It looks like it's having trouble showing up here, at least on my browser.

3. The attempt at a solution

Since this is a statics problem, I'm assuming all that is necessary is to set up equations so that the sum of all Forces, and the sum of all Torques, are each zero. I've immediately got a problem with the forces being zero, since the only horizontal force I can see is that of P.

With respect to Torque, I've tried the problem by putting the axis at C (which takes gravity out of the picture leaving me with only force P), B (which gives me a nice torque due to gravity of Rmgcos[Theta] but P is nullified, since it is parallel to it's position relative to B), and A (which, of course, takes P out of the equation).

Clearly, I'm missing something conceptually, because in my current way of thinking about the problem, there is no equilibrium short of at [Theta] = pi/2 -- when it can't rotate anymore!

Last edited: Jul 24, 2008