Calculate the moment of inertia of a uniform solid cone

[ehilge]

Homework Statement

Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo)

Homework Equations

I know I need to somehow use the equation I=[tex]\intr²dm[/tex]
also, I have an equation from my proffessor, dm=$$\rho$$dv I'm not sure if I need this though since its unifrom density so it doesn't seem like $$\rho$$ should matter.

The Attempt at a Solution

I don't have a solution right now. I know the answer is 3/10 MR² but I don't know how to het there. From class, since we did some examples, I think I need an equation that has a triple integral in it but I don't know what to integrate and to where.

Thanks for your help. Also, if you have any general suggestions on how to complete moment of inertia problems like this that would be great. I know we're going to be doing a lot of them.

Thanks again!

 

[alphysicist]

Hi ehilge,

Homework Statement

Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo)

Homework Equations

I know I need to somehow use the equation I=[tex]\intr²dm[/tex]

To put this in tex, don't use the [noparse][/noparse]. Use the caret ^, and put a space before the r, like this:

[noparse]$$\int r^2 dm$$[/noparse]

which gives:

$$\int r^2 dm$$

also, I have an equation from my proffessor, dm=$$\rho$$dv I'm not sure if I need this though since its unifrom density so it doesn't seem like $$\rho$$ should matter.

Yes, you'll need some form of the density. The integral has a dm in it, and you need to use the density function to change that to a dx, dA, dV, etc. (depending on the type of shape) so that you can perform the integration.

The Attempt at a Solution

I don't have a solution right now. I know the answer is 3/10 MR² but I don't know how to het there. From class, since we did some examples, I think I need an equation that has a triple integral in it but I don't know what to integrate and to where.

Thanks for your help. Also, if you have any general suggestions on how to complete moment of inertia problems like this that would be great. I know we're going to be doing a lot of them.

Thanks again!

If you look here

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mig

and scroll to near the bottom you will see links to three examples. Does that help?

If you get stuck on the cone calculation, post your work and where you are getting stuck and maybe someone can help.

 

[ehilge]

I was able to get the problem figured out. Thanks for your suggestions and also with the help with formatting.