Statics with an engine regulator

AI Thread Summary
The discussion focuses on a physics homework problem involving the relationship between angular speed and angle in a system with a counterweight performing uniform circular motion. The key equation derived is ω² cos(θ) = (1 + 2m'/m) g/L, which relates angular speed (ω) and angle (θ) under specific conditions. Participants suggest using separate vertical equations for the masses involved to solve the problem correctly. The initial attempt at a solution is acknowledged, but further clarification and steps are encouraged for accuracy. The conversation emphasizes the importance of systematic analysis in solving statics problems.
hurrfdurrf
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Homework Statement


[PLAIN]http://img15.imageshack.us/img15/7379/unledtzc.png
(The rods are of length L, there is no friction, massless rods, yadee yadee yada)
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}

Homework Equations


T_1 = L m \omega^2
\cos{\theta} (T_1 - T_2) = g (m + m')

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
 
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welcome to pf!

hi hurrfdurrf! welcome to pf! :wink:

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

what do you get? :smile:​
 

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