The formula to calculate the Product of Inertia is:
\[ Ixy = \sum m \cdot x \cdot y \]
Where:
Let's say an object has a mass of 10 kg, the distance from the y-axis to the object's center of mass is 2 meters, and the distance from the x-axis to the object's center of mass is 3 meters. The product of inertia would be calculated as follows:
\[ Ixy = 10 \cdot 2 \cdot 3 = 60 \text{ kg.m²} \]
So, the product of inertia is 60 kg.m².
Product of inertia is a measure of the asymmetry of a mass distribution about an axis. It is a mathematical property of a body’s mass distribution, calculated as the integral of the product of the mass of each particle and the square of its perpendicular distance from the axis. It is used in physics and engineering to predict the rotational behavior of rigid bodies. If the product of inertia is zero, it indicates that the mass distribution is symmetric about the axis.
