We were discussing the concept of Torsion or twisting
moment, Power transmitted by a circular solid shaft and
power transmitted by a circular hollow shaft in our previous posts.

Now we are going further to start a new topic i.e. Polar
moment of inertia with the help of this post. we will also see here the polar moment of inertia for various sections in this post.

###
**
So, what is polar moment of inertia?**

Polar moment of inertia of a plane area is basically
defined as the area moment of inertia about an axis perpendicular to the plane
of figure and passing through the center of gravity of the area.

Polar moment of inertia will be displayed by J.

Mathematically, we can write polar moment of inertia
i.e. J as mentioned here.

We can also say from above equation of polar moment
of inertia that, Polar moment of inertia of an element will be basically the
resultant of the product of element area and square of its distance from the
axis.

Polar moment of inertia is basically a quantity
which is used to specify the body resistance against twisting and it also
suggests the strength of body against torsion loading.

Polar moment of inertia is quite similar to area
moment of inertia. We must have to note it here that both are used in design
analysis but area moment of inertia will be under consideration when structure
will be subjected with bending or deflection, while polar moment of inertia
will be under consideration when structure will be subjected with torsional
loading.

### Polar moment of inertia for various sections

We will now derive the torsional equation, in the
category of strength of material, in our next post.

### Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google