Appendix A-Moment of Inertia

����������� Tocompute the moment of inertia for a torus being revolved around the z axis, theequation I=(�R²+r²)M can be used, where R is the majorradius, 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/m³with a major radius of 2000 meters, and a minor radius of 255 (including theradiation shield), the moment of inertia can be found.� Thus the approximated moment of inertia is7.868x10¹⁷ kg·m².

Calculation

Volume of torus: V=2π²Rr²

I₁=(�R²+r₁²)·M= [�·(2000m)²+(255m)²]·100kg/m³·2π²·2000m·(255m)²