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Using the moments of inertia calculated in the previous post for the hemisphere (and taking for granted those of the cylinder), we can now determine those of a spherocylinder.

**UPDATE 22/08/2014**: Corrected a misprint in the formula for \(I_x\). See comment below.]Using the moments of inertia calculated in the previous post for the hemisphere (and taking for granted those of the cylinder), we can now determine those of a spherocylinder.

The height of the cylinder is \(h\), while its radius (and that of the spherical caps) is \(R\).

\(I_z\) is easy to determine by summing the corresponding moments of the cylinder and of the two hemispheres: \(I_z= \rho \, m_c \frac{R^2}{2} + 2 \rho \, m_h \frac{2}{5} R^2\). Developing \(m_c\) and \(m_h\) and introducing the aspect ratio \(\gamma = 1+ \frac{h}{2R}\) yields:

\[I_z = \pi \rho R^5 \left [ (\gamma -1) + \frac{8}{15} \right ] \]

\[I_z = \pi \rho R^5 \left [ (\gamma -1) + \frac{8}{15} \right ] \]