Product of Inertia :-

• Product of inertia (POI) is a feature of an object that describes an imbalance relative to a defined set of coordinate axes.

• If the mass of the object is distributed symmetrically with respect to the XY, YZ, and ZX planes, then the POI in all three planes is zero.

• However, if the mass is not distributed symmetrically, the result is a non-zero POI causing an imbalance when the object is rotated.

• One way to better understand POI is to think of a tire on a vehicle. Tires need to be balanced on both the inside of the tire as well as the outside — otherwise, the vehicle can be unsafe to drive. When a tire is perfectly balanced, the weight of the wheel is distributed evenly around it and between the outside of the rim and the inside.

Importance of Product of Inertia :-

The concept of the product of inertia plays an important role in the study of the rotational motion of bodies. The magnitudes of the pressure forces on the bearings on which the axial shaft of a body rotates depend on the values of the products of inertia. The pressures will be minimal—that is, equal to the static pressures—if the axis of rotation is a principal axis of inertia that passes through the center of mass of the body.