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you should be able to do in this course,
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be able to take some body, slice it up in some fashion,
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and find the location of the center of mass.
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You combine symmetry arguments with actual calculation.
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For this sliver, by symmetry,
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you know the center of mass is at the center,
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you don't waste your time,
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but then when you add these guys
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there is no further symmetry you can use;
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you have to do the actual work.
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So, what have I done so far?
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What I've done is point out to you