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IEVref: | 113-03-21 | ID: | |

Language: | en | Status: Standard | |

Term: | moment of inertia | ||

Synonym1: | mass moment of inertia [Preferred] | ||

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Symbol: | JI
| ||

Definition: | for a body and a specified axis, scalar quantity equal to the integral J = ∫_{D} R^{2} dm = ∫_{D} R^{2} ρ dV, where ρ is mass density in a domain D with quasi-infinitesimal mass dm and volume dV, and R is the distance between the domain and the axisNOTE 1 For a material point, the moment of inertia is equal to the product of its mass NOTE 2 In non-relativistic physics, moment of inertia is an additive quantity. NOTE 3 More generally, moment of inertia can be defined for a rigid body as a tensor quantity $\overrightarrow{\overrightarrow{J}}$, where NOTE 4 The moment of inertia is not to be confused with the second axial moment of area and the second polar moment of area. NOTE 5 The coherent SI unit of moment of inertia is kilogram metre squared, kg·m | ||

Publication date: | 2011-04 | ||

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Internal notes: | 2014-07-11: Corrected <i>J</i>, <i>I</i> to <i>J</i><br><i>I</i>. JGO 2017-06-02: Cleanup - Remove Attached Image 113-03-21en.gif | ||

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NOTE 1 For a material point, the moment of inertia is equal to the product of its mass *m* and the square of its distance *R* to the axis, thus *J* = *mR*^{2}. For a system of particles, it is equal to the sum of their moments of inertia.

NOTE 2 In non-relativistic physics, moment of inertia is an additive quantity.

NOTE 3 More generally, moment of inertia can be defined for a rigid body as a tensor quantity $\overrightarrow{\overrightarrow{J}}$, where *J*_{xx} = −∫(*y*^{2} + *z*^{2}) d*m*, cycl., cycl., and *J*_{yz} = −∫ *yz* d*m*, cycl. cycl.

NOTE 4 The moment of inertia is not to be confused with the second axial moment of area and the second polar moment of area.

NOTE 5 The coherent SI unit of moment of inertia is kilogram metre squared, kg·m^{2}.