Analytical Mech Homework Solutions 106

Analytical Mech Homework Solutions 106 - 4 R = (x + y 2 1...

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4 () 1 1 22 2 2 R xy b z =+ = 1 2 1 2 b dR dz z  =   1 1 2 2 2 0 1 2 2 b z b I Rd v b z b z bz d z z ρρπ == ∫∫ 0 1 6 b z 5 I bb z z d z b π ρπ =− = ρ 1 1 2 2 0 1 2 2 b b md v b z b z z d z 3 0 1 2 b mb b z d z b = 2 1 3 z I mb = (e) α is the half-angle of the apex of the cone. r is the radius of the base at z = 0 and is radius of a circle at some arbitrary z in a plane parallel to the base. D r , a constant tan R R z D bz dv RhdR ππ R zdR b D Since R = , , and the limits of integration for correspond to zb R b D R dR dz b D 0 R R =→ D 0 2 2 0 2 2 2 z bzR I v z −− DD R b 4 32 23 4 4 1 3 b z R 4
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