### Main Difference

Moment of Inertia and Polar Moment of Inertia are both the quantities expressing a body’s tendency to resist changes when certain torque is being applied. Moment of Inertia is often refereed as mass moment of inertia or the angular mass. It is the measure of an object’s resistance against the angular acceleration. The resistance being done here is against the rotation rate when certain torque is applied. On the other hand, Polar Moment of Inertia is a measure of a body’s ability to resistance against the torsion when torque is being applied. It is utilized to calculate the angular displacement of a body subjected to torque.

### Comparison Chart

 Moment of Inertia Polar Moment of Inertia Definition A quantity expressing a body’s tendency to resist angular acceleration is known as the Moment of Inertia. Polar Moment of Inertia is measure of an object’s ability to resist torsion under specified axis when and torque is being applied. Mathematical Representation The mathematical representation of Moment of Inertia is $I=\int r^2\:\mathrm dm$. Polar Moment of Inertia can be defined mathematically as $I=\int r^2\:\mathrm dA$ . Units In Moment of Inertia units of kg m2 are used for measuring. In polar moment of Inertia units of m4 are used for measuring.

### What is Moment of Inertia?

A quantity expressing a body’s tendency to resist angular acceleration is known as the Moment of Inertia. Angular accelerations is 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 capacity of the cross-section to resist bending. Actually it is body’s resistance to changes to its rotation when a torque is being applied. It will be relevant to mention here that torque is a force that tends to cause rotation, whereas moment of inertia is measure of an object’s resistance against the possible angular rotation.

### What is Polar Moment of Inertia?

Polar Moment of Inertia is measure of an object’s ability to resist torsion under specified axis when and torque is being applied. Torsion is a widely known term used in field of solid mechanics, it generally expresses the twisting of object due to an applied torque. It is utilized to calculate the angular displacement of a body subjected to torque. Higher the polar moment of Inertia, the less the object will twist after torque is applied.The polar moment of area can be utilized to calculate the moment of inertia with arbitrary cross-section. “Polar Moment of Inertia is also called “Second Moment of Area“, “Area Moment of Inertia“, “Polar Moment of Area” or “Second Area Moment“.

### Moment of Inertia vs. Polar Moment of Inertia

• A quantity expressing a body’s tendency to resist angular acceleration is known as the Moment of Inertia, whereas Polar Moment of Inertia is measure of an object’s ability to resist torsion under specified axis when and torque is being applied.
• Polar Moment of Inertia is utilized 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 arbitrary cross-section.
• The mathematical representation of Moment of Inertia is $I=\int r^2\:\mathrm dm$ , while Polar Moment of Inertia can be defined mathematically as $I=\int r^2\:\mathrm dA$ .
• In Moment of Inertia units of kg m2 are used for measuring, on the other hand, in polar moment of Inertia units of m4 are used for measuring.  