Enter the mass, distance from the y-axis, and distance from the x-axis into the calculator to determine the product of inertia.

## Product of Inertia Formula

The following formula is used to calculate the product of inertia.

Ixy = Σ m * x * y

Variables:

• Ixy is the product of inertia (kg.m²) m is the mass of the object (kg) x is the distance from the y-axis to the object’s center of mass (m) y is the distance from the x-axis to the object’s center of mass (m)

To calculate the product of inertia, multiply the mass of the object by the distance from the y-axis to the object’s center of mass, then multiply the result by the distance from the x-axis to the object’s center of mass. Sum up these products for all the objects.

## What is a Product of Inertia?

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.

## How to Calculate Product of Inertia?

The following steps outline how to calculate the Product of Inertia using the given formula:

1. First, determine the mass of the object (m) in kilograms.
2. Next, determine the distance from the y-axis to the object’s center of mass (x) in meters.
3. Next, determine the distance from the x-axis to the object’s center of mass (y) in meters.
4. Multiply the mass (m) by the distance from the y-axis (x) and the distance from the x-axis (y).
5. Finally, calculate the Product of Inertia (Ixy) using the formula Ixy = Σ m * x * y.

Example Problem:

Use the following variables as an example problem to test your knowledge:

mass of the object (m) = 5 kg

distance from the y-axis to the object’s center of mass (x) = 2 m

distance from the x-axis to the object’s center of mass (y) = 3 m