By Team Aakash Byju's | 21st December 2022
Detailed Explanation
Consider the image where a rod of mass M and length L is given
I =
ML
12
c
2
The moment of inertia of the rod along the axis passing through its centre is given as
M
Moment of Inertia of a Rod
Now, to find the moment of inertia of the rod perpendicular to its axis, we need to consider the Parallel Axis Theorem.
I = I +
Md
c
2
Where d is the distance between the two axes.
M
Moment of Inertia of a Rod
In the image it is evident that the distance between the centre of the axis to one of its ends is .
L
2
M
Moment of Inertia of a Rod
So, the Parallel Axis Theorem can be written as
ML
2
M
I =
12
+ M
L
2
2
( )
ML
2
I =
12
+
ML
2
4
=
I =
ML
2
+
3ML
2
12
4ML
2
12
=
ML
2
3
Moment of Inertia of a Rod