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So, the momentum of the center of mass
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is the sum of the momentum of the two parts,
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but what you're learning is --
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so let me write it one more time -- if F external is equal to 0,
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then p1 + p2 does not change with time.
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This is a very, very basic and fundamental property,
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and it's in fact another result that survives all the revolutions
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of relativity and quantum mechanics,
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where what I've said for two bodies
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is true for ten bodies;
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you just do the summation over more terms.
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So, let me say in words what I'm saying.