Center of mass and Moment of Intertia

[sally21]

Homework Statement

The thickness of the object is 2 cm. The density of the material (pronounced row) is 7800. The angle (theta) is pi/6. The radius is .75 meters. What is the moment of inertia and
the center of mass?

Here is what the object looks like:

http://www13.zippyshare.com/v/36721619/file.html

The object is rotating around the origin.

Homework Equations

None given

The Attempt at a Solution

Okay, so I have no idea how to find the center of mass for this object. I know you have to use integration, but the other kid in my class was using triple integration (which is something I don't know and I don't know if he was right any way). So I have no idea how to find the center of mass for this object.

As for the moment of inertia, I think that the moment of inertia will be 1/12 of the moment of inertia of a cylinder. I figure this because pi/6 = 30 degrees. 360/30=12. So I think that the moment of inertia will be:

I= 1/2m[(r1^2)+(r2^2)] * 1/12

this is just the moment of inertia formula for a hollow cylinder and I multiplied it by 1/12.

Thank you very much for helping me in any way!

 

[ideasrule]

Okay, so I have no idea how to find the center of mass for this object. I know you have to use integration, but the other kid in my class was using triple integration (which is something I don't know and I don't know if he was right any way). So I have no idea how to find the center of mass for this object.

You don't need triple integration. Instead of using x,y,z coordinates, use "r" instead. You can integrate dm*r, then divide the result by the mass to get the r coordinate of the center of mass.

As for the moment of inertia, I think that the moment of inertia will be 1/12 of the moment of inertia of a cylinder. I figure this because pi/6 = 30 degrees. 360/30=12. So I think that the moment of inertia will be:

I= 1/2m[(r1^2)+(r2^2)] * 1/12

this is just the moment of inertia formula for a hollow cylinder and I multiplied it by 1/12.

That's not right. Think about it this way: if we fill in the missing 11/12 of the cylinder, the cylinder's mass would be 12m.

 

[sally21]

Oh thank you!

But, I don't really understand how to find the moment of inertia and now I don't know how to find the center of mass. Can you show me how to find it for this problem? I have no idea what dm is.

 

[sally21]

bumb

anyone know how to solve this?