Utente:Andrea And/Sandbox/3: differenze tra le versioni

Versione delle 15:13, 5 lug 2012

Versione delle 09:33, 6 lug 2012

Riga 68:

Also, it can be taken to be made up of infinitesimally thin, hollow spheres, where the radius differs from 0 to ''r''.

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| [[right angle|RightCono]] circularcircolare [[coneAngolo (geometry)retto|coneretto]] con radiusraggio ''r'', heightaltezza ''h'' e massa ''m''

|align="center"| [[Image:moment of inertia cone.svg|120px]]

|<math>I_z = \frac{3}{10}mr^2 \,\!</math>&nbsp;&nbsp;<ref name="beer">{{cita libro

Riga 97:

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| ThinPiastra rectangularrettangolare platesottile di altezza ''h'' e di, larghezza ''w'' e massa ''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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| ThinPiastra rectangularrettangolare platesottile di altezza ''h'' e di, larghezza ''w'' e massa ''m''

|align="center"| [[Image:Recplane.svg]]

|<math>I_c = \frac {m(h^2 + w^2)}{12}\,\!</math>&nbsp;&nbsp;<ref name="serway"/>

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| [[Parallelepipedo]] solido di altezza ''h'', larghezza ''w'', e profondità ''d'', e massa ''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>

| For a similarly oriented [[cube (geometry)|cube]] con sides of length <math>s</math>, <math>I_{CM} = \frac{m s^2}{6}\,\!</math>.

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| [[Parallelepipedo]] solido di altezza ''D'', larghezza ''W'', e lunghezza ''L'', e massa ''m'' con theasse longestlungo diagonalla asdiagonale thepiù axislunga.

|align="center"| [[Image: Moment of Inertia Cuboid.jpg|140px]]

|<math>I = \frac{m\left(W^2D^2+L^2D^2+L^2W^2\right)}{6\left(L^2+W^2+D^2\right)}</math>

| ForPer aun cubecubo condi sideslato <math>s</math>, <math>I = \frac{m s^2}{6}\,\!</math>.

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| PlanePoligono [[polygon]]piano con verticesvertici <math>\vec{P}_{1}</math>, <math>\vec{P}_{2}</math>, <math>\vec{P}_{3}</math>, ..., <math>\vec{P}_{N}</math> e

massa <math>m</math> uniformemente distribuita, che ruota intorno a un asse perpendicolare al piano e passante per l'origine.

mass <math>m</math> uniformly distributed on its interior, rotating about an axis perpendicular to the plane e passing through the origin.

|align="center"| [[Image:Polygon moment of inertia.png|130px]]

|<math>I=\frac{m}{6}\frac{\sum\limits_{n=1}^{N-1}\|\vec{P}_{n+1}\times\vec{P}_{n}\|((\vec{P}_{n+1}\cdot\vec{P}_{n+1})+(\vec{P}_{n+1}\cdot\vec{P}_{n})+(\vec{P}_{n}\cdot\vec{P}_{n}))}{\sum\limits_{n=1}^{N-1}\|\vec{P}_{n+1}\times\vec{P}_{n}\|}</math>

|Questa espressione assume che theil polygonpoligono issia [[star-shaped polygon|star-shaped]]. The vectors <math>\vec{P}_{1}</math>, <math>\vec{P}_{2}</math>, <math>\vec{P}_{3}</math>, ..., <math>\vec{P}_{N}</math> are [[position vector|position vectors]] of the vertices.

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| Infinite [[disk (mathematics)|disk]] con mass [[normally distributed]] on two axes around the axis of rotation