# Difference Between Moment of Inertia and Polar Moment of Inertia: Notes pdf ppt Engineering Mechanics

## Main Difference – Moment of Inertia vs. Polar Moment of Inertia:

**Moment of inertia** (which refers to the *mass **second moment* of inertia) and **polar (second) moment of inertia** are both quantities which describe an object’s ability to resist changes due to torques applied to it. The **main difference** between moment of inertia and polar moment of inertia is that the **moment of inertia measures how an object resists angular acceleration**, whereas the **polar moment of inertia measures how an object resists torsion**.

## What is Moment of Inertia:

Moment of inertia for a body is defined with the following integral:

where is the distance of the mass element from the axis of rotation.

Physically, the moment of inertia gives the ability of a body to resist angular acceleration (analogous to how mass resists linear acceleration) when subject to a torque. If the moment of inertia is large, then the angular acceleration produced by a given torque would be smaller. The **unit of moment of inertia** is **kg m ^{2}**.

Moment of inertia is used to calculate rotational kinetic energy and also to calculate torque in terms of mass and angular acceleration.

## What is Polar Moment of Inertia:

Polar second moment of inertia gives an object’s ability to resist *torsion* (i.e. “twisting”) about a given axis due to an applied torque. If the polar moment of inertia is large, the torsion produced by a given torque would be smaller. Polar moment of inertia is defined as:

where is the distance of the *area *element from the axis of rotation. The **unit of polar moment of inertia** is **m ^{4}**.

**Polar second moment of area** is often confused with the area second moment of inertia, which is defined:

where is the distance of the area element from a specific *plane*. This also has units of m^{4}, however physically this quantity indicates the resistance of an object to *bend* about a certain plane when subjected to a torque.

## Difference Between Moment of Inertia and Polar Moment of Inertia:

## Mathematical definition of Moment of Inertia and Polar Moment of Inertia:

**Moment of inertia** is defined as

**Polar moment of inertia** is defined as

## Physical Meaning:

**Moment of inertia** is a measurement of an object’s resistance to angular acceleration.

**Polar moment of inertia** is a measurement of an object’s resistance to torsion (twisting).

## Units:

**Moment of inertia** is measured in units of kg m^{2}.

**Polar moment of inertia** is measured in units of m^{4}.