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So, let me say in words what I'm saying.
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Take a collection of bodies.
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At a given instant everything is moving;
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it's got its own velocity and its momentum,
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add up all the momenta.
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If you had one dimension, just add the numbers.
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If in two dimensions, add the vectors;
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you get a total momentum.
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That total momentum does not change
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if there are no outside forces acting on it.
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So, a classic example is two people are standing on ice.
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Their total momentum is 0 to begin with,