Calculating Inertia

Discussion in 'Math' started by Qhorin, Apr 17, 2009.

  1. Qhorin

    Thread Starter New Member

    Apr 17, 2009

    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)? :confused:
  2. jasperthecat


    Mar 26, 2009

    A picture often helps

    Have a look at this site

    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

  3. Qhorin

    Thread Starter New Member

    Apr 17, 2009
    Thanks for the reply. I think I understand it now, I just had the picture wrong in my head:)