I'm wondering what the product of inertia is. What I mean is this, while I know the mathematical formula for it, I don't understand the underlying concept. For instance, I understand the moment of inertia, 'I', because I can relate it to the kinetic energy of rotation of a body. I also understand it in terms of rotation about an axis. So that, 1/2mv^2 = 1/2mwr^2 .... where v = wr, v is the linear velocity, w the angular velocity, and r the radius, or radial distance, of a point from the center of rotation of the body. So, I = mr^2 for each mass unit of the body, or in integral form: I = ∫ r^2 dm However, the product of inertia isn't clear to me. I don't see the relation to kinetic energy or rotation (what's the axis of rotation?). My text gives a rather thin explanation for it. Can anyone give a concrete description of what it is, with examples? Many thanks for any help.