Conservation of angular momentum.

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Angular momentum is conserved around the bottom left corner of the described system because there are no external torques acting on it. The setup involves a square and a leaping mass, with the center of mass being crucial for analysis. Gravity, while acting on the system, does not exert a torque about the bottom left corner due to its line of action passing through that point. This means that the gravitational force does not create a moment arm, thus not affecting angular momentum conservation. Understanding these principles clarifies why angular momentum remains conserved in this scenario.
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Why is angular momentum conserved around the bottom left corner in the following set up (see attachment)? The attachment shows a square of side a and mass 4m, and a body of mass m leaping with velocity v0 as shown in the attachment towards the opposite side of the square. I have found the new center of mass of the system but do not quite understand why there would be no external torques in action around the bottom left corner. I'd appreciate some insight.
 

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There seems to be no external forces to produce any external torques.
 
What about gravity, acting downwards from the new center of mass (of the body that has leaped and reached the opposite side of the square and the square)? With respect to the bottom left corner, why won't gravity exercise a torque?
 

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