The values of this proper
The values of this property along certain lines are the semi-major axes of the Poinsot ellipse; the colatitude partial derivative of this quantity is zero along those lines, which are known as geometric principle axes.  For planar translations, this property transforms by Steiner's theorem, which can be derived directly when one considers this quantity as a contravariant rank-two symmetric tensor. Its magnitude is equal to an object's area of gyration times its mass. For 10 points, identify the material property that is equal to the integral over a body of distance from an axis with respect to mass, is symbolized I, and is the rotational analogue of mass.
The values of this property along certain lines are the semi-major axes of the Poinsot ellipse; the colatitude partial derivative of this quantity is zero along those lines, which are known as geometric principle axes.  
mass {moment} of {inertia} [prompt on I before it's mentioned]