Physics

# Difference Between Moment of Inertia and Polar Moment of Inertia

Main difference

Moment of Inertia and Polar Moment of Inertia are the two quantities that express the tendency of a body to resist changes when a certain torque is applied. The moment of inertia is often called the moment of inertia of mass or angular mass. It is the measure of an object’s resistance against angular acceleration. The resistance that is made here is against the speed of rotation when a certain torque is applied. On the other hand, the polar moment of inertia is a measure of the body’s ability to resist twisting when a torque is applied. It is used to calculate the angular displacement of a body subjected to torque.

## Comparison chart

 Moment of inertia polar moment of inertia Definition A quantity that expresses the tendency of a body to resist angular acceleration is known as the moment of inertia. The polar moment of inertia is a measure of an object’s ability to resist twisting about a specified axis when a torque is applied. mathematical representation The mathematical representation of the moment of inertia is$I = int r ^ 2 : mathrm dm$. The polar moment of inertia can be defined mathematically as$I = int r ^ 2 : mathrm dA$. Units In Moment of Inertia, the units of kg m 2 are used to measure. In the polar moment of inertia, the units of m 4 are used to measure.

## What is the moment of inertia?

A quantity that expresses the tendency of a body to resist angular acceleration is known as the moment of inertia. The angular accelerations are the sum of the products of the mass of each body with the square of its distance from the axis of rotation. It is also defined as the ability of the cross section to resist bending. It is actually the body’s resistance to changes in its rotation when a torque is applied. It will be relevant to mention here that torque is a force that tends to cause rotation, while moment of inertia is the measure of an object’s resistance against possible angular rotation.

## What is the polar moment of inertia?

The polar moment of inertia is a measure of an object’s ability to resist twisting about a specified axis when a torque is applied. Torsion is a widely known term used in the field of solid mechanics, generally expressing the twisting of an object due to an applied torque. It is used to calculate the angular displacement of a body subjected to torque. The higher the polar moment of inertia, the less the object will twist after the torque is applied. The polar moment of area can be used to calculate the moment of inertia with an arbitrary cross section. “ The polar moment of inertia is also called “ second moment of area ”, “ moment of area of ​​inertia ”, “ polar moment of area”or“ second moment of area ”.

## Moment of inertia versus polar moment of inertia

• A quantity that expresses the tendency of a body to resist angular acceleration is known as the Moment of Inertia, while the Polar Moment of Inertia is the measure of an object’s ability to resist torsion about a specified axis when a force is applied. pair.
• The polar moment of inertia is used to calculate the angular displacement of a body subjected to torque.
• The polar moment of area can be used to calculate the moment of inertia with an arbitrary cross section.
• The mathematical representation of the Moment of Inertia is$I = int r ^ 2 : mathrm dm$, while the Polar Moment of Inertia can be defined mathematically as$I = int r ^ 2 : mathrm dA$.
• In Moment of Inertia, units of kg m 2 are used to measure, on the other hand, in Polar Moment of Inertia units of m 4 are used to measure.