Moment of Inertia of a Thin Rod
The moment of inertia (I) of a thin rod rotating about an axis perpendicular to the rod and passing through its center is given by:
* I = (1/12) * M * L²
Where:
* M is the mass of the rod
* L is the length of the rod
Doubling the Length
If you double the length of the rod (L becomes 2L), the moment of inertia becomes:
* I' = (1/12) * M * (2L)² = (1/12) * M * 4L² = 4 * (1/12) * M * L²
Conclusion
Therefore, when the length of the thin rod is doubled, the moment of inertia increases by a factor of four. This makes sense because the moment of inertia depends on the square of the length. As the length increases, the mass is distributed further away from the axis of rotation, resulting in a greater resistance to changes in angular motion.
