Statics with an engine regulator

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SUMMARY

The discussion focuses on the relationship between angular speed (\(\omega\)) and angle (\(\theta\)) in a system involving a counterweight performing uniform circular motion. The derived equation is \(\omega^2 \cos{\theta} = (1 + \frac{2m'}{m}) \frac{g}{L}\), where \(g\) is the acceleration due to gravity, \(L\) is the length of the rods, and \(m'\) is the mass of the counterweight. Participants emphasize the need for separate vertical force equations for both masses to validate the solution approach.

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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 [itex]\omega[/itex], the counterweight performs uniform circular motion. Show that [itex]\omega[/itex] and [itex]\theta[/itex] are related as follows:

[itex]\omega^2 \cos{\theta} = (1 + \frac{2m'}{m}) \frac{g}{L}[/itex]

Homework Equations


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

The Attempt at a Solution


(Working backwards) Combined above to get
[itex]T_2 \cos{\theta} = m' g[/itex]

which makes a lot of sense, but I'm not sure if the procedure was right
 
Last edited by a moderator:
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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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