Conservation of angular momentum.

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SUMMARY

Angular momentum is conserved around the bottom left corner of the described system due to the absence of external torques. In the scenario involving a square of side 'a' and a mass '4m', with an additional mass 'm' leaping with velocity 'v0', the gravitational force acts through the center of mass and does not create a torque about the bottom left corner. The analysis confirms that since there are no external forces producing torques, angular momentum remains conserved throughout the motion.

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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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