15_5_27 - 27. is the spherical shell, x 2 + y 2 + z 2 = a 2...

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27. is the spherical shell, x 2 + y 2 + z 2 = a 2 , with areal density σ . Its mass is 4 πσ a 2 . Its moment of inertia about the z -axis is I = σ ZZ ( x 2 + y 2 ) dS = σ Z 2 π 0 d θ Z π 0 a 2 sin 2 φ a 2 sin φ d φ = 2 πσ a 4 Z π 0 sin φ( 1 - cos 2 φ) d φ Let u = cos
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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