University Physics with Modern Physics with Mastering Physics (11th Edition)

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8.110: By symmetry, 0 = cm x . Using plane polar coordinates leads to an easier integration, and using the Theorem of Pappus ( 29 ( 29 3 3 4 2 cm π π 2 2 a y a = π is easiest of all, but the method of Problem 8.109 involves Cartesian coordinates. For the x -coordinate, dx x a t dm 2 2 - = ρ , which is an even function of x, so = . 0 dx x For the y -coordinate,
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Unformatted text preview: y a ρt dm 2 2 2-= , and the range of integration is from 0 to a , so ∫-= a dy y a y M ρt y 2 2 cm . , 2 Making the substitutions , 2 , , π 2 2 2 2 1 y du y a u t a ρ M-=-= = and π 3 4 π 3 4 π 2 2 3 2 2 1 2 cm 2 2 a u a du u a y a o a = -=-= ∫ ....
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