Find the moment of inertia of a washer

[Pablo]

Homework Statement

Find moment of inertia of a washer with a hole of radius r/2.

Homework Equations

Moment of inertia = integral of x^2 dm
γ = m / L

The Attempt at a Solution

I think I can find the moment of inertia of the washer using integral of x^2 dm. So, I know my γ = m / L = m / (R/2) = 2m / R

I = (2m / R) * [((R/2)^3 / 3) - 0] = (m * R^2) / 12

However, that is not correct. Where am I going wrong?

 

[berkeman]

Is there a diagram that shows the washer's dimensions? Is it a thick washer or a thin washer?

Also, you can find a LaTeX tutorial under INFO at the top of the page. Click on Help/How-To. That will help you post with math equations that are much easier to read and respond to.

 

[haruspex]

γ = m / L

What are γ and L? This looks like an expression for linear density, but a washer has area.

 

[Dr Dr news]

This looks like a three-dimensional problem. What is your expression for dm?

 

[haruspex]

This looks like a three-dimensional problem. What is your expression for dm?

No, I think it is just a lamina. No thickness is given.