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Unformatted text preview: m = R R z ρπ r 2 dz m since dm = ρπ r 2 dz = R R z ρπ ( R 2z 2 ) dz m since r 2 = R 2z 2 = ρπ R 4 4 m = ρπ R 4 4(2 ρπ R 3 / 3) since m = 1 2 ρ 4 3 π R 3 = 3 R 8 i.e., the center of mass of a hemisphere is 3 R / 8 from the base Using these for ﬁnding the center of mass of the composite body, z C = ∑ m i z i ∑ m i = ± ρ π R 2 H 3 ² ( H 4 ) + ± ρ 2 π R 3 3 ² (3 R 8 ) ± ρ π R 2 H 3 ² + ± ρ 2 π R 3 3 ² = R 2 H 2 12 = R 4 4 H 2 = 3 R 2 H = R √ 3 2...
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 Spring '10
 richard
 Mass, Trigraph, Archimedes, Fundamental physics concepts, Jaguar Racing

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