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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 radius of the disk is R, and the mass of the disk is M. Using the parallel axis theorem and theequation for the moment of inertia of a disk about its central axis developed in the previous example, Eq. (8), the moment of inertia of the disk about the specified axis is Fig.