# Template:Physeq1/MomentOfInertia

 Description Figure Moment(s) of inertia Point mass m at a distance r from the axis of rotation. $I=mr^{2}$ 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) $I_{\mathrm {end} }={\frac {mL^{2}}{3}}\,\!$ Rod of length L and mass m $I_{\mathrm {center} }={\frac {mL^{2}}{12}}\,\!$ Thin circular hoop of radius r and mass m $I_{z}=mr^{2}\!$ $I_{x}=I_{y}={\frac {mr^{2}}{2}}\,\!$ Thin cylindrical shell with open ends, of radius r and mass m $I=mr^{2}\,\!$ Solid cylinder of radius r, height h and mass m $I_{z}={\frac {mr^{2}}{2}}\,\!$ $I_{x}=I_{y}={\frac {1}{12}}m\left(3r^{2}+h^{2}\right)$ Sphere (hollow) of radius r and mass m $I={\frac {2mr^{2}}{3}}\,\!$ Ball (solid) of radius r and mass m $I={\frac {2mr^{2}}{5}}\,\!$ Thin rectangular plate of height h and of width w and mass m (Axis of rotation at the end of the plate) $I_{e}={\frac {mh^{2}}{3}}+{\frac {mw^{2}}{12}}\,\!$ Solid cuboid of height h, width w, and depth d, and mass m $I_{h}={\frac {1}{12}}m\left(w^{2}+d^{2}\right)$ $I_{w}={\frac {1}{12}}m\left(h^{2}+d^{2}\right)$ $I_{d}={\frac {1}{12}}m\left(h^{2}+w^{2}\right)$ 