Moment of inertia of a rectangular door hinged on long side

[ahello888a]

Homework Statement

Determine the moment of inertia of a 19kg door that is 2.5m high and 1.1m wide and is hinged along long side. Ignore the thickness of the door

Homework Equations

I=$$\int$$ (R^2 dm)

The Attempt at a Solution

I really don't know where to start with this problem. My book only shows me how to do moments for cylindrically shaped objects and rods, so i don't know how to deal with 2d objects. I'm having particular trouble with coming up with a dm that is reliant on R.

 

[mgb_phys]

The general definition of moment of intertia is to consider a small part of the object with mass dm at a distance r and sum the product of r*r dm.
So for the door, imagine splitting the door into thin vertical slices, then calculate the mass of the slice and the square of the distance from the hinge.
If you know calculus you can do this analytically and come up with an equation - that's what the integral you have given calculates

 

[ahello888a]

i still have absolutely no clue how to do this. can you point to an example or something?

 

[ahello888a]

never mind...