Hi,

I'm having a little problem understanding a few examples on my current homework. The problem I get stuck on sounds like this:

"Find the moment of inertia for a circular cylinder of base radius a and height h about a diameter of the cylinder. The density, δ, is constant."

I know I should use cylindrical coordinates and I'm given the formula for the moment of inertia (I = ∫∫∫D^2*δ dV; Where D is the perpendicular distance from the volume element dV to the axis of rotation.) After that I'm stuck.

I checked the answer in my solution manual and the integral is supposed to look like this: δ∫∫∫ (x^2+z^2). Therefore I assume that D^2 = sqrt(x^2+z^2). Why is that? Shouldn't it be sqrt(x^2+y^2+z^2)?

 

Qhorin

A picture often helps

Have a look at this site
http://hyperphysics.phy-astr.gsu.edu/Hbase/mi.html#cmi

There are others as well

You are rotating a cylinder around its centre and it is made up of many very thin disks going out h/2 each side where it is being rotated. The sqrt(x^2+z^2) is the radius of the circle that is being swept out to create the discs.

BTW sqrt(x^2+y^2+z^2) is more related to a sphere.

Hope this helps you start

J

 

Thanks for the reply. I think I understand it now, I just had the picture wrong in my head