Analytical Mech Homework Solutions 109

Analytical Mech Homework Solutions 109 - 7 m = h ( ab ) Iz...

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7 mh () a b ρπ = 22 4 z m I ab =+ For an ellipsoid: , dv hdxdy = 222 R xy = + and on the surface, 1 xyz abc ++= 1 2 1 zc    2b 2a y x 1 2 1 hzc == −− In the xy plane 1 += 1 2 2 2 1 y xa b z 1 2 2 2 1 2 2 2 1 1 2 2 1 21 y yb b z y b I R dv x y c dxdy ρρ =− = == + ∫∫ 11 2 2 2 z ca y a y I ax x d x y b ρ =    +     d x From a table of integrals: 3 24 2 22 2 1 sin 48 8 x kx k x kxx d x k −= + + 2 1 sin x kxd x k + 2 42 2 2 82 b z b ca y a y I yd b ππ + y 4 4 2 2 2 1 4 b z b ay y y I ac y dy bb b + + 4 15 z I abc a b For an ellipsoid, 4 3 m abc = , so 5 z m I 7
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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