The easiest derivation of rod's moment of inertia?

[Glyper]

Homework Statement

Derive the formula for rod's moment of inertia: I = ml²/12

Homework Equations

I = ml²/12

The Attempt at a Solution

The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some easier (or more "natural"?) way to do it? Or, if not, maybe you know some website where it's explained as if I were five so that I can get the grasp of it? Because looking at bare integrals, I don't quite know what I'm calculating.

 

[rock.freak667]

I think the easiest way would be to just do the integral.

I= ∫ r² dm

If you consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod, the mass of this piece will be dm.

Then you just use the fact that mass = mass per unit length * distance i.e. dm = M/L * dr

 

[Glyper]

I see. Thanks :)