|Definition:|| for a body and a specified axis, scalar quantity equal to the integral J = ∫D R2 dm = ∫D R2 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 axis|
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 = mR2. 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 , where Jxx = −∫(y2 + z2) dm, cycl., cycl., and Jyz = −∫ yz dm, 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·m2.