Problems and solutions I

The internal torques cancel for all pairs of charges

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.

Ask a homework question - tutors are online