Determine the moment of inertia of a homogeneous disc with density $\rho_0$ of radius R with a circular hole of radius R/2 and central radius R/2 regarding an axis perpendicular to the surface and going through the center of gravity.
Alright, first I tried drawing the situation, because I don't think I understood it correctly from reading the problem.
Here's what I was thinking:
At first I thought the axis would go through the center of the disc, but then I read that it's going through the center of gravity. But since it says central radius R/2 regarding an axis ... through the center of gravity does that mean that the center of gravity is at a distance R/2 away from the boundary of the hole?
I'm just not sure about the use of words in this problem. Is kind of hard to figure out the actual problem.
And how would I even get the moment of inertia just by knowing the center of gravity? I mean, yeah, it's the axis around which it rotates but I never dealt with an object with a hole in some random part of it.
By the way, can I assume that the mass is $2\pi R^2\cdot \rho_0$? Since the disc doesn't have an actual volume, or maybe it has, but the thickness of the disc is not given, so I'm uncertain about that.
I would appreciate any help.