# M2: moments when forces are not perpendicular

1. Feb 16, 2010

### pianogirl

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

A smooth uniform rod AB, of length 3a and weight 2w, is pivoted at A so that it can rotate in a vertical plane. A light ring is free to slide along the rod. A light inextensible string is attached to the ring and passes over a fixed smooth peg at a point C, a height 4a above A, and carries a particle of weight w hanging freely.
a) Give reasons why in equilibrium, the string will be at right angles to the rod.
b) show that the angle theta that the rod makes to the vertical in equilibrium is given by tan theta= 4/3
c) Find the magnitude of the force of the pivot on the rod A in terms of w.

2. Relevant equations

Moment stuff like M= Fd and in equil., total anticlockwise moments= total clockwise moments.

3. The attempt at a solution
Well, I drew a diagram.
For part b, I tried doing moments around A to get Tension in the string= 2w sin theta.
When I did sohcahtoa, I got tan theta= 4w sin theta/3a.

And basically, I'm confused.
Help would be appreciated!
Thanks!

2. Feb 16, 2010

### tiny-tim

Hi pianogirl!
How did you get this? The tension holding the weight w in equilibrium is just w.

3. Feb 16, 2010

### pianogirl

Oh yeah! Totally forgot that. Thanks! Will try again!