6.C6 I = 7.84 x lOll kg-m 2 Yendcaps I =J(2rr (100) (100) (.3) (.2000) (6 (100) 2 + (100) 2 ) Ydirt = 2.20 x 10 11 kg-m 2 I Y3 housing torus }(Mass of torus) (4(Major radius) 2 +5(Minor radius) 2 ) ½(3xl0 5 ) (4(100) 2 +5(5) 2 ) = 1.50 x 10 9 kg-m 2 By the parallel axes theorem, I + 2 (I + (Mass of torus) (60) 2 ) Yhousing Y3 I Y4 torus of machinery = ½(3xl0 6 ) (4(50) 2 +5(15) 2 ) = 4.17 x 10 9 kg-m 2 By the parallel axes theorem, 5.17 x 10 9 kg-m 2 I Ymachinery 9.47 x lOlO kg-m2 I Yatmosphere cylinder f2(Mass of cylinder) (3(Radius) 2 +(Length) 2 ) = 5.14 x 10 9 kg-m 2 The center of mass of a solid hemisphere is on its axis of symmetry, ¾(Radius) away from the sphere-center. From the parallel axes theorem, I = I - (Mass hemisphere) <¾(.Radius)) 2 Y5 Y1 where I }(Mass hemisphere) (Radius) 2 Y1
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