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it will do that.
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What I'm now telling you is,
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if I take a complex body
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made of 20,000 parts,
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all connected to each other pushing and pulling,
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if you fling that crazy thing in the air,
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it'll do all kinds of gyrations and jiggling as it moves around.
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But if you found its center of mass,
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the center of mass will follow simply a parabola,
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because the external force on it is just M·g.
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So, it'll be M·R two dots equals m·g
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and that's just motion with constant acceleration