Physics equations/Equations/Moments of inertia (large table)

Description	Figure	Moment(s) of inertia
Point mass m at a distance r from the axis of rotation.		$I=m{r}^2$
Two point masses, M and m, with reduced mass $\mu$ and separated by a distance, x.		$I=\frac{Mm}{M+m}{x}^2=\mu x^2$
Rod of length L and mass m (Axis of rotation at the end of the rod)		$I_{\mathrm{e}\mathrm{n}\mathrm{d}}=\frac{m{L}^2}{3}$
Rod of length L and mass m		$I_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}=\frac{m{L}^2}{12}$
Thin circular hoop of radius r and mass m		$I_z=m{r}^2$ $I_x=I_y=\frac{m{r}^2}{2}$
Thin cylindrical shell with open ends, of radius r and mass m		$I=m{r}^2$
Solid cylinder of radius r, height h and mass m		$I_z=\frac{m{r}^2}{2}$ $I_x=I_y=\frac{1}{12}m(3r^2+h^2)$
Sphere (hollow) of radius r and mass m		$I=\frac{2m{r}^2}{3}$
Ball (solid) of radius r and mass m		$I=\frac{2m{r}^2}{5}$
Thin rectangular plate of height h and of width w and mass m (Axis of rotation at the end of the plate)		$I_e=\frac{m{h}^2}{3}+\frac{m{w}^2}{12}$
Solid cuboid of height h, width w, and depth d, and mass m		$I_h=\frac{1}{12}m(w^2+d^2)$ $I_w=\frac{1}{12}m(h^2+d^2)$ $I_d=\frac{1}{12}m(h^2+w^2)$