# Difference between moment of inertia and moment of polar inertia

Difference between moment of inertia and moment of polar inertia: Moment of inertia and Moment of polar 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 mass moment of inertia or angular mass. It is the measure of the resistance of an object against the angular acceleration.

The resistance 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 torsion when a torque is applied. It is used to calculate the angular displacement of a body subjected to torque.

## Key Differences

- 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 the ability of an object to resist torsion under a specified axis when a pair.
- The polar moment of the area can be used to calculate the moment of inertia with an arbitrary cross section.
- The polar moment of inertia is used to calculate the angular displacement of a body under torque.
- In Moment of Inertia, the units of kg m 2 are used to measure, on the other hand, in the polar moment of Inertia, units of m 4 are used to measure.
- The mathematical representation of the Moment of inertia is
**(put formula)**, while the Polar Moment of Inertia can be defined mathematically as I = int r ^ 2: mathrm dA.

## Difference between moment of inertia and moment of polar inertia in Tabular Form

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. | Polar moment of inertia is a measure of an object’s ability to resist torsion under a specified axis when torque is applied. |

Units | In Moment of inertia, the units of kg m 2 are used to measure. | At the polar moment of inertia, the units of m 4 are used to measure. |

Mathematical representation | The mathematical representation of the moment of inertia is I = int r ^ 2: mathrm dm. | The polar moment of inertia can be mathematically defined as I = int r ^ 2: mathrm dA. |

## 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 torque is applied. It will be relevant to mention here that torque is a force that tends to cause rotation, while the moment of inertia is the measure of the resistance of an object against possible angular rotation.

## What is the polar moment of inertia?

Polar moment of inertia is a measure of an object’s ability to resist torsion under a specified axis when torque is applied. Torsion is a widely known term used in the field of solid mechanics, it generally expresses the torsion of an object due to an applied torque.

It is used to calculate the angular displacement of a body subjected to torque. The greater the polar moment of inertia, the less the object will twist after torque is applied.

The area polar moment 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 the area ”.