# Polar moment of inertia vs Moment of inertia – Difference

Polar moment of inertia vs moment of inertia can differentiate as the polar moment of inertia shows the resistance offered by an object to deformation by torsional load and the moment of inertia shows the resistance offered by a cross-section of the object to the deformation (caused by bending load).

## What is polar moment of inertia?

The Polar moment of inertia is associated with the cross-section of an object that shows the resistance offered by an object to deformation caused by torsional loading.

It is one of the types of the second moment of area that is generally denoted by the symbol ‘J’.

The SI unit of the polar moment of inertia is m⁴ and the FPS unit is Ft⁴.

From the above diagram, the Polar moment of inertia about the z-axis is given by,

J_{Z} = \int r².dA

## What is moment of inertia?

The moment of inertia shows the distribution of cross-sectional area from a specific reference axis. It is also known as the planar moment of inertia and it is one of the types of the second moment of area.

The moment of inertia represents the amount of resistance offered by the cross-section to the deflection due to the bending loads.

It is generally denoted by the symbol ‘ 𝙸 ‘ and the reference axis for finding a moment of inertia always lies in a planar surface.

For the cross-section shown in the above figure, the moment of inertia about the x-axis is given by,

I_{\text{xx}} = \int y².dA

And the moment of inertia of the above cross-section about the y-axis is given by,

I_{yy} = \int x².dA

## Difference between moment of inertia and polar moment of inertia:

FAQ’s

1. What is the difference between moment of inertia and polar moment of inertia?

The moment of inertia states the resistance offered by the cross-section for the bending load and the polar moment of inertia states the resistance offered by the cross-section of the object to the torsional load.

2. How moment of inertia is related to polar moment of inertia?

The relation between the moment of inertia and the polar moment of inertia can be given by using the perpendicular axis theorem.
J𝗈 = 𝙸𝗑 + 𝙸𝗒
Where,
J𝗈 = Polar moment of inertia
𝙸𝗑 and 𝙸𝗒 = Moment of inertia about mutually perpendicular axes (x and y axis) which are lying in the plane of cross-section.

3. What is the relationship between moment of inertia I and polar moment of inertia J for a circular section?

For circular cross-section, the relationship between the moment of inertia and polar moment of inertia is given by,
Polar moment of inertia (J) = 2 x (Moment of inertia about centroid)
As 𝙸 = (π/64)D⁴
∴ J = (π/32)D⁴ = 2 x (π/64)D⁴ = 2 𝙸