# Appendix A-Moment of Inertia

** **To
compute the moment of inertia for a torus being revolved around the z axis, the
equation I=(¾R^{2}+r^{2})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 R_{1}=minor radius.
Assuming the colony is a solid torus with density 100 kg/m^{3}
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
7.868x10^{17} kg·m^{2}.

## Calculation

Volume of torus: V=2π^{2}Rr^{2}

I_{1}=(¾R^{2}+r_{1}^{2})·M
= [¾·(2000m)^{2}+(255m)^{2}]·100kg/m^{3}·2π^{2}·2000m·(255m)^{2}

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