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Here's a simple example;
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you can show that if this mass and that mass are equal,
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and say this one is at rest, that one comes and hits this.
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You can show under certain conditions this one will come to rest
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and this will start moving with the speed of the--
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the target will move at the speed of the projectile.
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So, momenta of individual objects have changed.
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One was moving before, it is not moving;
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one was at rest, it's moving,
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but when you add up the total, it doesn't change.
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This is called the Law of Conservation of Momentum.
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So, that's so important