Moment of inertia

The sum of the products formed by multiplying the mass (or sometimes, the area) of each element of a figure by the square of its distance from a specified line.

Source:Service de « Travaux publics et Services gouvernementaux Canada »

Formulas

Moment of inertia in relation to an axis (Δ) :

By definition the moment of inertia IΔ in relation to an axis Δ, of a material point with a mass m, located at a distance r from Δ, is : I_\Delta=mr^2

The moment of inertia in relation to Δ of a system, composed of N material points, with masses mi, located at a distance ri from axis D, is : I_\Delta=\sum_{i=1}^Nm_ir_i^2

For a solid made of an infinity of material points, the limit is : I_\Delta=\lim_{N\rightarrow\infty}\sum_{i=1}^Nm_ir_i^2=\int r^2dm

Moment of inertia in relation to a point : The moment of inertia of a body in relation to a point O is equal to the half-sum of its moments of inertia in relation to three perpendicular axis (Ox, Ox, Oz) all passing through the point O. I_O = ( I_{Ox} + I_{Oy} + I_{Oz} ) / 2