Solve Rigid Body Collision: System Approach w/Cons. Angular Momentum

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Discussion Overview

The discussion revolves around the conditions under which a rigid body collision problem can be approached using the conservation of angular momentum, particularly focusing on the validity of applying this principle about different points during two-body collisions.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the validity of using the conservation of angular momentum about a point fixed in a massless extension of a rigid body or its mass center during rigid body collisions.
  • Another participant asserts that torque, defined as the rate of change of angular momentum, is valid about any axis, although they note that the equation τ = Iα is only applicable for axes through the center of mass or center of rotation.
  • A third participant emphasizes that the conservation principles are only valid about axes fixed in inertial space.
  • A later reply expresses agreement with the previous points raised.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of angular momentum conservation in rigid body collisions, with no clear consensus reached on the conditions under which it can be applied.

Contextual Notes

There are limitations regarding the assumptions about the axes of rotation and the nature of the collision, which remain unresolved in the discussion.

anandvineet27
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under what conditions can a rigid body collision problem be solved using a system approach, (i.e by using the conservation of angular momentum of the two rigid bodies about some point)
the equation M=d[H]/dt is only valid when M and H are taken about a point fixed in a massless extension of a rigid body or its mass center. Yet for two-body collision problems, I have seen the total angular momentum being conserved about some point,( say, if a ball collides with a rod, then the cg of the rod).Is this approach valid?
 
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welcome to pf!

hi anandvineet27! welcome to pf! :smile:

torque = rate of change of angular momentum (τ = dL/dt) is valid about any axis :wink:

(however, τ = Iα is valid only for an axis through the centre of mass or centre of rotation)
 
only valid about axes fixed in an inertial space.
 
yes :smile:
 

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