Moment of Inertia of a Thin Rod
Moment of Inertia of a Thin Rod about the Axis Perpendicular to the Length and Passing through the Center
Take a uniform thin rod AB whose mass is M and length is l. YY’ axis passes through the center of the rod and perpendicular to the length of the rod. We have to calculate the moment of inertia about this axis YY’.
Fig: Moment of Inertia of a thin rod about the perpendicular axis along its length
Suppose, small piece dx is at a distance x from the YY’ axis. Hence, mass of length dx is = \(\left(\frac{M}{l}\right)\) dx
The moment of inertia of small piece about the YY’ axis
dl = \(\left[\left(\frac{M}{l}\right) d x\right] x^{2}\)
Therefore, the moment of inertia of the complete rod about the YY’ axis.
