To compute the moment of inertia for a torus being revolved around the z axis, the equation I=(¾R2+r2)M can be used, where R is the major radius, r is the minor radius, and M is the total mass of the torus, or ρV [ref 47]. In the below equations, R= major radius and R1=minor radius. Assuming the colony is a solid torus with density 100 kg/m3 with a major radius of 2000 meters, and a minor radius of 255 (including the radiation shield), the moment of inertia can be found. Thus the approximated moment of inertia is 7.868x1017 kg·m2.
Volume of torus: V=2π2Rr2
I1=(¾R2+r12)·M = [¾·(2000m)2+(255m)2]·100kg/m3·2π2·2000m·(255m)2
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