Angular momentum extended body

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SUMMARY

The discussion focuses on calculating the angular momentum of a system consisting of two slender rods colliding, specifically relative to their center of mass. The participants clarify that the formula L = Iω is not applicable without knowing the point of measurement for angular velocity. Instead, they emphasize using the center of mass as the origin for computing angular momentum, suggesting that transforming the diagram to a frame where the center of mass is at rest simplifies the calculation. The key takeaway is that the total angular momentum can be viewed as the sum of angular momentum due to the motion of the center of mass and the angular momentum about the center of mass.

PREREQUISITES
  • Understanding of angular momentum concepts in physics
  • Familiarity with the center of mass calculations
  • Knowledge of rigid body dynamics
  • Basic proficiency in using formulas related to angular motion
NEXT STEPS
  • Study the derivation of angular momentum formulas for rigid bodies
  • Learn about the principles of center of mass in multi-body systems
  • Explore the concept of reference frames in physics
  • Investigate the effects of collisions on angular momentum conservation
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding angular momentum in multi-body systems, particularly in collision scenarios.

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Suppose I have the system on the attached file, where two slender rods collide. I want to calculate the angular momentum of the system before collision relative to the center of mass of the two rods. I'm however not sure how to do this. definitely the formula L=Iw doesn't apply, since I don't know from which point I should measure the angular velocity. Equivalently I don't know where what R to use if I use the formula: L = mvR. It seems intuitive if it was the center of mass, but why it is, I have no idea. Who can explain what R to use and why?
 

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You can always treat the total angular momentum of a system as composed of the angular momentum due to the motion of its center of mass plus the angular momentum about its center of mass.

If you wish to use the center of mass as your origin for computing angular momentum, just transform your first diagram to a frame in which the center of mass is at rest. Since neither rod is rotating (at first), all you have to worry about is the motion of each rod's center of mass.
 

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