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

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A rigid body collision problem can be solved using a system approach by applying the conservation of angular momentum about a fixed point, such as the center of gravity of one of the bodies involved. The equation M = d[H]/dt is applicable when considering angular momentum about a point fixed in a massless extension of a rigid body or its mass center. Torque, defined as τ = dL/dt, is valid for any axis, but the equation τ = Iα holds true only for axes through the center of mass or center of rotation. This means that while total angular momentum can be conserved in two-body collision problems, careful consideration of the reference point is essential. The discussion emphasizes the importance of using appropriate axes for accurate calculations in rigid body collisions.
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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