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to derive the moment of inertia of a solid sphere of uniform density and radius R. [tex] dI = r_{\perp}^{2} dm = r_{\perp}^{2} \rho dV [/tex] â. where [itex] r_{\perp} [/itex] is the perpendicular distance to a point at r from the axis of rotation. Therefore, [itex] r_{\perp} = |\mathbf{r}|\sin{\theta} [/itex].
The first equation I came across shows my moment of inertia as: I = pi/64(D^4-d^4) where; D= outer diameter of pipe. d= inner diameter of pipe. I have also come across another equation for moment of inertia in a paper regarding HDD installation loading and stress analysis. This equation is to find the pulling load within a curved section of HDD. They used moment of inertia to ultimately determine the Normal forces applied to the pipe.