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Is conservation of angular momentum a direct consequence of conservation of linear momentum? It seems like it is. Here is a short proof I derived.

Assume that we have a particle moving in space with constant (conserved) momenum p. The particle's position is given by x(t) = x0 + t/m * p. The angular momentum of the system is given by L(t) = r(t) x p = x0 x p + t/m * p x p. By antisymmetry, the second term, p x p is zero, so L(t) = x0 x p, which is constant. Therefore, angular momentum is conserved.

Assuming my proof is correct for this case, does this proof work in a general case?

It seems that the reverse would also be true.... that conservation of angular momentum implies the conservation of angular momentum.

Assume that we have a particle moving in space with constant (conserved) momenum p. The particle's position is given by x(t) = x0 + t/m * p. The angular momentum of the system is given by L(t) = r(t) x p = x0 x p + t/m * p x p. By antisymmetry, the second term, p x p is zero, so L(t) = x0 x p, which is constant. Therefore, angular momentum is conserved.

Assuming my proof is correct for this case, does this proof work in a general case?

It seems that the reverse would also be true.... that conservation of angular momentum implies the conservation of angular momentum.

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