Calculate polar moment of inertia

Section 21

Polar moment of inertia

It is called the moment of inertia of a system of material points in relation to a plane, an axis or a pole, the sum of the products between the masses of the particles that make up the system and the square of the distances of these particles to the plane, axis or pole considered:

Compared to a Cartesian reference system we have:

• polar moments of inertia:

The polar moment of inertia can be calculated as:

• the semisum of the axial moments of inertia in relation to three rectangular axes passing through that point:

• the sum of planar moments of inertia:

• the sum of the moments of inertia in relation to a plane and a normal axis to that plane: