View source for Physics equations/Equations/Moments of inertia (large table)

[[Category:Physics equations/Equations]]

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! Description<ref>https://en.wikipedia.org/w/index.php?title=List_of_moments_of_inertia&oldid=582953751</ref>  
|| Figure  || Moment(s) of inertia 
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| Point mass ''m'' at a distance ''r'' from the axis of rotation.
|align="center"|
| <math> I = m r^2</math>
|-
| Two point masses, ''M'' and ''m'', with [[reduced mass]] ''<math> \mu </math>'' and separated by a distance, ''x''.
|align="center"|
| <math> I = \frac{ M m }{ M \! + \! m } x^2 = \mu x^2 </math>
|-
| [[Rod (geometry)|Rod]] of length ''L'' and mass ''m'' <br>(Axis of rotation at the end of the rod)
| align="center"|[[Image:moment of inertia rod end.svg]]
| <math>I_{\mathrm{end}} = \frac{m L^2}{3} \,\!</math>
|-
| [[Rod (geometry)|Rod]] of length ''L'' and mass ''m''
| align="center"|[[Image:moment of inertia rod center.svg|170px]]
| <math>I_{\mathrm{center}} = \frac{m L^2}{12} \,\!</math>
|-
| Thin circular [[hoop]] of radius ''r'' and mass ''m''
| align="center"|[[Image:moment of inertia hoop.svg|170px]]
| <math>I_z = m r^2\!</math><br><math>I_x = I_y = \frac{m r^2}{2}\,\!</math>
|-
| Thin [[cylinder (geometry)|cylindrical]] shell with open ends, of radius ''r'' and mass ''m''
|align="center"| [[Image:moment of inertia thin cylinder.png]]
| <math>I = m r^2 \,\!</math>
|-
|Solid cylinder of radius ''r'', height ''h'' and mass ''m''
|align="center"| [[Image:moment of inertia solid cylinder.svg|170px]]
|<math>I_z = \frac{m r^2}{2}\,\!</math><br><math>I_x = I_y = \frac{1}{12} m\left(3r^2+h^2\right)</math>
|-
| [[Sphere]] (hollow) of radius ''r'' and mass ''m''
|align="center"| [[Image:moment of inertia hollow sphere.svg|170px]]
|<math>I = \frac{2 m r^2}{3}\,\!</math>
|-
| [[ball (mathematics)|Ball]] (solid) of radius ''r'' and mass ''m''
|align="center"| [[Image:moment of inertia solid sphere.svg|170px]]
|<math>I = \frac{2 m r^2}{5}\,\!</math>
|-
| Thin rectangular plate of height ''h'' and of width ''w'' and mass ''m'' <br>(Axis of rotation at the end of the plate)
|align="center"| [[Image:Recplaneoff.svg]]
|<math>I_e = \frac {m h^2}{3}+\frac {m w^2}{12}\,\!</math>
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| Solid [[cuboid]] of height ''h'', width ''w'', and depth ''d'', and mass ''m''
|align="center"| [[Image:moment of inertia solid rectangular prism.png]]
|<math>I_h = \frac{1}{12} m\left(w^2+d^2\right)</math><br><math>I_w = \frac{1}{12} m\left(h^2+d^2\right)</math><br><math>I_d = \frac{1}{12} m\left(h^2+w^2\right)</math>
|}