The easiest derivation of rod's moment of inertia?

AI Thread Summary
The discussion focuses on deriving the moment of inertia formula for a rod, specifically I = ml²/12. One participant mentions using integration by dividing the rod into two parts, seeking a simpler or more intuitive method. They express difficulty in understanding the integration process and request resources that explain the concept in simpler terms. The integration approach involves calculating I as the integral of r² dm, where dm is defined as mass per unit length times an infinitesimal distance. The conversation emphasizes the need for clearer explanations to grasp the derivation effectively.
Glyper
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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.
 
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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
 
I see. Thanks :)
 

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