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you gain a factor of 2.
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So, take the simple case where I2 is half of I1
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and you will see it.
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Okay, so you can ask,
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"Where does that energy come from?
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How does this ice skater pick up speed,
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pick up angular momentum or kinetic energy?"
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The angular momentum doesn't change,
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but the rotational energy changes.
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Yep?
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You can do this without invoking any new concepts,
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using this old concept.