For this post, I want to prove that in the absence of external forces, the total angular momentum of an N-particle system is conserved.
I start with which is the total momentum of an N-particle system. Now I can vectorially multiple the total momentum by which is the position vector measured from the same origin for each particle. This will give me the total angular momentum of the system which can be written as . After differentiating with respect to , I obtain . In the first cross product, I can substitute with , and since the cross product of any two parallel vectors is zero, the first term becomes zero. This leaves implies that my sum becomes . Now, I can rewrite the net force on particle as , where represents the force exerted on particle by particle . Now I can make a substitution for to give me
…I will finish the rest of this at some point. I seem to have misplaced the book.