Conversion of translational momentum to angular momentum

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SUMMARY

The discussion focuses on the conversion of translational momentum to angular momentum in a system involving two masses, m1 and m2, connected by a rigid, massless bar of length L. When mass m1, traveling at velocity v0, collides with the bar at its center of mass, both masses move as a single system. The conservation of linear momentum and angular momentum principles are applied to derive the final translational and angular velocities, denoted as v1 and v2. The key to solving the problem lies in selecting an appropriate pivot point for calculating angular momentum.

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Suppose there was a mass, m1, traveling rightwards at v0. There is a second mass, m2, above the line of motion of m1, and which has a rigid, massless bar of length L attached to its center of mass. This bar extends downwards so that the terminal intersects with the path of m1. When m1 reaches this intersection, it attaches to the bar at its own center of mass, and m1 and m2 move as a single system. How can one find the resulting translational and angular velocities of the final system?
 
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Your title is misleading. Linear momentum and angular momentum are separately conserved. Let final velocities of m1 and m2 be v1 and v2. Write down equations embodying conservation of linear mometum and conservation of angular momentum. You will have to choose a point about which to calculate initial and final angular momenta.
 
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