Dielectric barrier discharge

List of 3D inertia tensors

This list of moment of inertia tensors is given for principal axes of each object.

Description	Figure	Moment of inertia tensor
Solid sphere of radius r and mass m	File:Moment of inertia solid sphere.svg	$I=\left[\begin{array}{ccc}\frac{2}{5}m{r}^2& 0& 0\\ 0& \frac{2}{5}m{r}^2& 0\\ 0& 0& \frac{2}{5}m{r}^2\end{array}\right]$
Hollow sphere of radius r and mass m	File:Moment of inertia hollow sphere.svg	$I=\left[\begin{array}{ccc}\frac{2}{3}m{r}^2& 0& 0\\ 0& \frac{2}{3}m{r}^2& 0\\ 0& 0& \frac{2}{3}m{r}^2\end{array}\right]$
Solid ellipsoid of semi-axes a, b, c and mass m	File:Ellipsoide.png	$I=\left[\begin{array}{ccc}\frac{1}{5}m(b^2+c^2)& 0& 0\\ 0& \frac{1}{5}m(a^2+c^2)& 0\\ 0& 0& \frac{1}{5}m(a^2+b^2)\end{array}\right]$
Right circular cone with radius r, height h and mass m, about the apex	File:Moment of inertia cone.svg	$I=\left[\begin{array}{ccc}\frac{3}{5}m{h}^2+\frac{3}{20}m{r}^2& 0& 0\\ 0& \frac{3}{5}m{h}^2+\frac{3}{20}m{r}^2& 0\\ 0& 0& \frac{3}{10}m{r}^2\end{array}\right]$
Solid cuboid of width w, height h, depth d, and mass m	180x 180x	$I=\left[\begin{array}{ccc}\frac{1}{12}m(h^2+d^2)& 0& 0\\ 0& \frac{1}{12}m(w^2+d^2)& 0\\ 0& 0& \frac{1}{12}m(w^2+h^2)\end{array}\right]$
Slender rod along y-axis of length l and mass m about end	File:Moment of inertia rod end.svg	$I=\left[\begin{array}{ccc}\frac{1}{3}m{l}^2& 0& 0\\ 0& 0& 0\\ 0& 0& \frac{1}{3}m{l}^2\end{array}\right]$
Slender rod along y-axis of length l and mass m about center	File:Moment of inertia rod center.svg	$I=\left[\begin{array}{ccc}\frac{1}{12}m{l}^2& 0& 0\\ 0& 0& 0\\ 0& 0& \frac{1}{12}m{l}^2\end{array}\right]$
Solid cylinder of radius r, height h and mass m	File:Moment of inertia solid cylinder.svg	$I=\left[\begin{array}{ccc}\frac{1}{12}m(3r^2+h^2)& 0& 0\\ 0& \frac{1}{12}m(3r^2+h^2)& 0\\ 0& 0& \frac{1}{2}m{r}^2\end{array}\right]$
Thick-walled cylindrical tube with open ends, of inner radius r1, outer radius r2, length h and mass m	File:Moment of inertia thick cylinder h.svg	$I=\left[\begin{array}{ccc}\frac{1}{12}m(3({r_1}^2+{r_2}^2)+h^2)& 0& 0\\ 0& \frac{1}{12}m(3({r_1}^2+{r_2}^2)+h^2)& 0\\ 0& 0& \frac{1}{2}m({r_1}^2+{r_2}^2)\end{array}\right]$

See also

• Moment of inertia
• List of moments of inertia
• List of area moments of inertia
• The inertia tensor of a triangle in three-dimensional space

External links

• The inertia tensor of a tetrahedron