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== List of 3D inertia tensors ==
This list of [[Moment of inertia#The inertia tensor|moment of inertia tensor]]s is given for [[principal axes]] of each object.

{|class="wikitable"
|-
! Description !! Figure !! Moment of inertia tensor
|-
| Solid [[sphere]] of radius ''r'' and mass ''m'' 
|| [[Image:moment of inertia solid sphere.svg|180px]]
|| <math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
|Hollow sphere of radius ''r'' and mass ''m''||[[Image:moment of inertia hollow sphere.svg|180px]]||
<math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
| Solid [[ellipsoid]] of semi-axes ''a'', ''b'', ''c'' and mass ''m'' 
|| [[Image:Ellipsoide.png|180px]]
|| <math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
| [[Right circular cone]] with radius ''r'', height ''h'' and mass ''m'', about the apex
|| [[Image:moment of inertia cone.svg|180px]] 
|| <math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
| Solid cuboid of width w, height h, depth d, and mass m 
|| [[Image:moment of inertia solid rectangular prism.png|180x|center]]
|| <math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
|Slender rod along y-axis of length ''l'' and mass ''m'' about end|| [[Image:Moment of inertia rod end.svg|center]]||
<math>
I =
\begin{bmatrix}
  \frac{1}{3} m l^2  & 0 & 0 \\
  0 & 0 & 0 \\
  0 & 0 & \frac{1}{3} m l^2 
\end{bmatrix}
</math>
|-
|Slender rod along y-axis of length ''l'' and mass ''m'' about center|| [[Image:Moment of inertia rod center.svg|180px|center]]||
<math>
I =
\begin{bmatrix}
  \frac{1}{12} m l^2  & 0 & 0 \\
  0 & 0 & 0 \\
  0 & 0 & \frac{1}{12} m l^2
\end{bmatrix}
</math>
|-
|Solid cylinder of radius r, height h and mass m|| [[Image:Moment of inertia solid cylinder.svg|180px]]||
<math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|-
|Thick-walled cylindrical tube with open ends, of inner radius ''r''<sub>1</sub>, outer radius ''r''<sub>2</sub>, length ''h'' and mass ''m''|| [[Image:Moment of inertia thick cylinder h.svg|180px]]||
<math>
I =
\begin{bmatrix}
  \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{bmatrix}
</math>
|}

==See also==

*[[Moment of inertia]]
*[[List of moments of inertia]]
*[[List of area moments of inertia]]
*[[Inertia tensor of triangle|The inertia tensor of a triangle in three-dimensional space]]

==External links==
*[http://number-none.com/blow/inertia/bb_inertia.doc The inertia tensor of a tetrahedron]

[[Category:Physical quantities]]
[[Category:Rigid bodies]]
[[Category:Tensors]]

[[he:טנזור התמד#טבלה]]