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Unformatted text preview: s are central forces; this is that F 12 , the force of mass 2
on mass 1, is directed parallel (or antiparallel) to the line between the masses. ””
F 12 ˛ Ir1 - r2 M ó Ir1 - r2 M ä F 12 = 0
Now when we sum the net torques we get a cancellation of the internal torques. The internal torques cancel for all pairs of charges. The
cancellation between m1 and m2 follows from ”
r1 ä F 12 + r2 ä F 21 = r1 ä F 12 + r2 ä I-F 12 M = Ir1 - r2 M ä F 12 = 0.
The other internal forces cancel similarly. We end up with
ext ext ext t1 + t2 + t3 = „
„t I L1 + L2 + L3 M . It should be clear how this could be generalized to four, or an arbitrary number, of particles. This gives the very fundamental result that for a
system of particles
ext tnet = „
„t Ltot . Conservation of Angular Momentum
The conservation of angular momentum follows from the expression above. If there are no external torques on a system then the total
angular momentum of the system is conserved. Chapter I - Rotational Dynamics and Equilibrium | 5 ext tnet = 0 ï „
„t Ltot = 0 ï D Ltot = 0 This derivation mirrors the conservation of linear momentum.
This is a very fundamental result. It has deep implications on the very large scale; in astrophysics it is crucial in the dynamics of pl...
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