How do I find the moment of inertia for shapes with uniform density?

[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.

answer: Will th answer be I=2M/a^2 (a^4/4)=Ma^2/2?

 

[matt grime]

1. that isn't the answer, no

I is the integral over A of pr^2 dA where p is the density and r is the distance from the origin


ie int over A of p(x^2+y^2)dxdy

the limits for x are -a/2 to a/2 and y is -b/2 to b/2

also use abp=M, I'm presuming you can do double integrals - this one is quite easy.

the second one is somewhat harder, but just try this for now.

 

[jlmac2001]

is this right

M(a^2/48+b^2/48) is the moment of inertia

 

[matt grime]

you're about a factor of 16 out, how did you get that? show your working...