IF I understand the concept (I've never heard of it before, either) it really isn't that complicated.Originally Posted by dadon
The formula for "second moment of inertia" ie. "second moment of area" (see Wikipedia) is where dA is an area element and y is the perpendicular distance from the axis of rotation and the area element. (Given this formula I am frankly wondering how it became known as a moment of inertia. It appears to have nothing at all to do with the concept!)
My only question is what exactly are we calculating the second moment of inertia for? The hoop, the disk, or the combination?
In any event, I can walk you through doing the integral (which is more or less trivial in any of the above cases.)
I will use area elements that are bits of hoops. So . If we are, for example, finding the moment of the disk we then integrate over all theta and all r from 0 to the radius of the disk, which I'm calling R:
So . To get the moments of the other objects, merely change the limits on the r integral.