Question

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through it's midpoint and perpendicular to its length is l its moment of inertia about an axis passing through one of its ends perpendicular to it's length is..?

Answer 1

Answer on Question #51295, Physics, Mechanics | Kinematics | Dynamics

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through it's midpoint and perpendicular to its length is $l$ its moment of inertia about an axis passing through one of its ends perpendicular to it's length is..?

Solution:

The moment of inertia of a rod of mass $M$ and length $L$ about an axis, perpendicular to its length, which passes through its midpoint is

$$I = \frac{1}{12} M L^2$$

This is a standard result. Using the parallel axis theorem, the moment of inertia about a parallel axis passing through one of the ends of the rod is

$$I' = I + M \left(\frac{L}{2}\right)^2 = \frac{1}{3} M L^2 = 4I$$

Answer: $I' = 4I$

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