Counterintuitive uniform bar torque question

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SUMMARY

The discussion centers on the behavior of a uniform bar pivoted at its center of mass, specifically when rotated to an angle theta greater than zero. Despite theoretical predictions of static equilibrium due to balanced torques, practical applications reveal that the bar often swings to a horizontal position. This phenomenon occurs because achieving an exact pivot at the center of mass is challenging in real-life scenarios, leading to variations in equilibrium orientation based on the pivot's actual location.

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The uniform bar in the attached diagram pivoted onto a wall on its center of mass and rotated an angle theta>0 from the horizontal should theoretically stay in static equilibrium because all torques are balanced, right?

How come trying to do this in real life usually leads to the bar swinging until the bar is horizontal?
 

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In real life, you rarely hit exactly the center of mass with a pivot. The real life equilibrium orientation will depend on where exactly the pivot is.
 

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