# Moment of inertia

1. Feb 19, 2004

### jlmac2001

I'm don't really know how to find the momemt of inertia. I have two questions that I'm stuck on.

Two questions:

1. Find the moment of inertia of a sheet f mass M and uniform density which is in the shape of a rectangle of sides a and b, for rotations about an axis passing through its center and perpendicular to the sheet.

answer:Will I start with this I= (integral over A)M/A dA? How would I find the limits of integration and integrate this?

2. Find the moment of inertia of a thin uniform disk of mass M and radius a for rotations about an axis through a diameter of the disk.

2. Feb 19, 2004

### Norman

$$\int r^2 dm = \int r^2 \sigma dA = \sigma \int r^2 dA$$

Where $\sigma$ is the constant density $\frac{M}{A}$

hope that helps

3. Feb 20, 2004

### jlmac2001

dnn't understand

could someone explain itto me?

4. Feb 20, 2004

### Norman

Re: Re: moment of inertia

$$\sigma \int r^2 dA =\sigma \int (x^2+y^2)dxdy$$

this is ok since if you draw the rectangle out, r is measured from the center of the plane and therefore $r^2=x^2+y^2$. Since the center of the plane is the axis of rotation... you should be able to figure out the limits of integration for x and y.
Cheers.