# Homework Help: Statics with an engine regulator

1. Jul 2, 2011

### hurrfdurrf

1. The problem statement, all variables and given/known data
[PLAIN]http://img15.imageshack.us/img15/7379/unledtzc.png [Broken]
At a certain angular speed $\omega$, the counterweight performs uniform circular motion. Show that $\omega$ and $\theta$ are related as follows:

$\omega^2 \cos{\theta} = (1 + \frac{2m'}{m}) \frac{g}{L}$
2. Relevant equations
$T_1 = L m \omega^2$
$\cos{\theta} (T_1 - T_2) = g (m + m')$

3. The attempt at a solution
(Working backwards) Combined above to get
$T_2 \cos{\theta} = m' g$

which makes a lot of sense, but i'm not sure if the procedure was right

Last edited by a moderator: May 5, 2017
2. Jul 2, 2011

### tiny-tim

welcome to pf!

hi hurrfdurrf! welcome to pf!

you need vertical equations for mass m and for mass m' (separately) …

what do you get?