What is the final angular velocity of a falling physical pendulum?

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SUMMARY

The final angular velocity of a falling physical pendulum, specifically a meter stick pivoted at the bottom, can be determined using the moment of inertia formula I = 1/12 ML² and the principles of conservation of energy. The discussion highlights the challenge of finding velocity information, suggesting that elliptic integrals may be involved in the calculations. The user seeks to relate this angular velocity to the force required to transition from a pushup position to standing.

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  • Understanding of moment of inertia, specifically I = 1/12 ML²
  • Familiarity with conservation of energy principles in physics
  • Basic knowledge of angular motion and velocity
  • Experience with elliptic integrals and their applications
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All --

With a meter stick standing straight up and pivoted at the *bottom*, what is
the final angular velocity as it hits the table?


I've found plenty of standard stuff on physical pendulums (meter stick
pendulum), where I = 1/12 MR^2, period, etc, but I can't find velocity info.


My dim recollection, and perhaps why I can't find the solution so quick, is
that an elliptic integral is involved??

The application is an interesting one:
I would like to approximate the force one would have to generate from a
pushup position sufficient to thrust one's self up to a standing position.

If I had the required Vo, I could probably figure stuff out from there.

I found some neat stuff, like the animations found in
http://www.myphysicslab.com/pendulum1.html ,
But, no velocity graph, and no physical pendulum. Otherwise well-done.


Any links, hints -- or solutions -- appreciated.

Thanks.
 
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Consider it to be a rod with MOI I=1/12 ML2, conservation of energy would work well here.
 

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