Use I=∫r2 dm to calculate I of a slender uniform rod of length L, about an axis at one end perpendicular to the rod. note: a "slender rod" often refers to a rod of neglible cross sectional area, so that the volume is the Length, and the mass density X Length.

The moment of inertia of a slender uniform rod of length L about an axis at one end perpendicular to the rod is .

Explanation:

Let be an uniform rod of length L whose origin is located at one one end and axis is perpendicular to the rod, such that:

Where:

- Linear density, measured in kilograms per meter.

- Mass of the rod, measured in kilograms.

- Distance of a point of the rod with respect to origin.

Mass differential can translated as:

The equation of the moment of inertia is represented by the integral below:

(as )

The moment of inertia of a slender uniform rod of length L about an axis at one end perpendicular to the rod is .