# Angular Momentum

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A uniform rod of mass m_1 and length L rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass m_2, are mounted so that they can slide along the rod. They are initially held by catches at positions a distance r on each side from the center of the rod, and the system is rotating at an angular velocity omega, w. Without otherwise changing the system, the catches are released, and the rings slide outward along the rod and fly off at the ends.

1. What is the angular speed of the system at the instant when the rings reach the ends of the rod?

2. What is the angular speed of the rod after the rings leave it?

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##### Solution Summary

This problem is a good example to understand the principle of conservation of angular momentum.

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Please see the attached file.

SOLUTION

Principle applicable : Conservation of angular momentum

Angular momentum (L) = Moment of inertia (I) x Angular velocity (ω)

See attached file for diagram.

1) Initial Moment of inertia = Moment of inertia of the rod + MI of ring 1 + MI of ring 2

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