6.C3 The human housing is modeled as two tori of mass 3xl0 5 kg each, of major radius 100 meters, minor radius 5 meters. I 2(¼(Mass of torus)l4(Major radius) 2 +3(Minor radius) 2 J 2 housing = 6.01 x 10 9 kg-rn 2 The workshops and machinery in the endcaps are modeled as tori of mass 3xl0 6 kg each (10 times the mass of the housing), major radius 50 meters, minor radius 15 meters. I 2 machinery 2 <¼ (3xl0 6 ) (4 (50) 2 +3 (15) 2 ) = 1.60 x lOlO kg-m 2 The atmosphere is modeled as a solid cylinder with solid hemispheres at its ends, of constant density .491 kg/m 3 (half o2 - half N 2 at 40530 N/m 2 and 295°K), with cylinder radius 100 meters, cylinder length 100 meters, and endcap radius 100 meters. ~(Mass cylinder) (Radius) 2 + ~(~ass endcaps) (Radius) 2 1(11 (100) 2 (100) (.491) (100) 2 ) 2 +~(1n(l00) 3 (./\91)) (100) 2 1.59 x 10 10 kg-m 2 The total moment of inertia is the sum of the moments of inertia of the components: I = 1.06 x 10 12 kg-m 2 2 hull
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