How Do You Calculate the Moment of Inertia for a Door?

[timnswede]

Homework Statement

A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges.

2. Homework Equations
I=∫x^2dm

The Attempt at a Solution

[/B]The way I set it up was that I made into strips of length H (height) and width dr. dm=λHdr, where λ is mass over the length, H. But when I do the integral ∫r^2λHdr from 0 to r, I end up with ⅓mr^3, but it should be ⅓mr^2. Is lambda supposed to m/rH? If so, can someone explain why please?

 

[Orodruin]

You can check this, in order for dm to be a mass, $\lambda$ must have dimensions of mass/length^2. It is the mass density per unit area of door.

 

[timnswede]

You can check this, in order for dm to be a mass, $\lambda$ must have dimensions of mass/length^2. It is the mass density per unit area of door.

Oh, well that makes sense, thank you. Sometimes I feel like it's the simplest things that I get stuck on.