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The only proof I've seen of Conservation of Angular Momentum assumes that the internal forces of the system act along the line joining particles i and j (i.e. - all internal forces are central.) Can we prove Conservation of Angular Momentum without this assumption?

If not, how can we apply conservation of angular momentum to systems that involve collisions, such as the following:

A uniform circular turntable is at rest in the $xy$ plane and is mounted on a frictionless axle, which lies along the vertical $ z$ axis. I throw a lump of putty (mass $m$) with speed $v$ toward the edge of the turntable. When the putty hits the turntable, it sticks to the edge, and the two rotate together with angular velocity $\omega.$ Find $\omega.$

Brett George
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    http://en.wikipedia.org/wiki/Noether's_theorem – lemon Oct 01 '14 at 16:59
  • When you threw the putty it exerted force on your arm. Your arm is attached to your body and feet. Your feet pushed on the ground imparting angular momentum to the ground. This balanced the angular momentum of the putty in flight. When the putty hits the table its angular momentum of flight transfers to the table. The table's angular momentum now balances the angular momentum of the ground, which was originally imparted to the ground by your feet. All the forces here are central. – DanielSank Oct 01 '14 at 17:31
  • You are confusing position vectors with force vectors. See the rigid body dynamics page. – user121330 Oct 01 '14 at 17:55
  • Apologies, I should have said another derivation uses position vectors and ignores internal forces. The derivation using forces appears much more complicated to me. – user121330 Oct 01 '14 at 18:15
  • Conservation of angular momentum can't be proved from Newtonian mechanics, because conservation of angular momentum is true in general, but Newtonian mechanics is not true in general. Conservation laws are fundamental. Newton's laws are not. –  Oct 01 '14 at 20:05
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    May be not much related with this qn but still... http://physics.stackexchange.com/questions/114466/apparent-violation-of-newtons-3rd-law-and-the-conservation-of-angular-momentum# –  Dec 21 '14 at 21:32

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