Today we will see here the determination
of moment of inertia of one uniform thin rod; we will derive here the equation
to express the moment of inertia for thin rod.

Before going ahead we must have to find
out few basic posts which will be related with determination of moment of
inertia for various cases such as mentioned here.

####
*Moment
of inertia for rectangular section*

####
*Moment
of inertia for the hollow rectangular section*

####
*Moment
of inertia for circular section*

####
*Moment
of inertia for the hollow circular section *

####
*Area
moment of inertia Radius
of gyration *

####
*Basic
principle of complementary shear stresses*

Now we will go further to
start our discussion to understand the method for determining
the moment of inertia of one uniform thin rod with
the help of this post.

Let us consider one uniform
thin rod as displayed in following figure. Let us consider one small strip of
length dx and at a distance x from the YY axis as shown in figure.

L= Length of uniform thin
rod

m= Mass of the uniform thin
rod per unit length

M = Total mass of the uniform
thin rod

M = m.L

dx= Length of small strip

x= Distance of small strip
from YY axis

###
*
Now we will determine the moment of
inertia of uniform thin rod about YY axis*

*Now we will determine the moment of inertia of uniform thin rod about YY axis*

Let us determine the mass of
the small strip and we can easily write here as

Mass of the small strip = (Mass
of the uniform thin rod per unit length) x (length of small strip)

Mass of the small strip =
m.dx

Moment of inertia of this
small strip about axis YY could be easily determined and we can write here the
following equation to represent the moment of inertia of this small strip about
axis YY.

Moment of inertia of small
strip about axis YY = (m. dx). x

^{2}
Moment of inertia of small
strip about axis YY = mx

^{2}dxNow we will integrate the above equation from 0 to L in order to secure the value of moment of inertia of entire uniform thin rod about axis YY.

Finally we can conclude that
moment of inertia of entire uniform thin rod about axis YY could be easily written
as mentioned here.

###
**I**_{YY} =ML^{2}/3

_{YY}=ML

^{2}/3

Where, M = m.L

Do you have any suggestions or any
amendment required in this post? Please write in comment box.

###
**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another article in our next
post i.e. Determination of moment of inertia of area under curve in our next
post.

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