Task: Text Categorization
Input (English): quantity is constant in the body frame of an object, but has a time dependence in the space frame given by the position times this quantity in the body frame times the inverse of the position. For a random object, finding this quantity involves taking the integral of an outer product. Half of the time derivative of this quantity is equal to the scalar virial. This quantity provides the coefficients of the axes in Poinsot's ellipsoid. Euler's equations has this quantity in a dot product with the time derivative of angular velocity. The products of this 2nd order symmetric tensor form the non-diagonal term in the tensor matrix while the principal ones of this tensor form the diagonal in the tensor matrix. Given this quantity for one axis, one can find it for another axis with the Parallel Axis theorem. For 10 points, name this quantity that for a hoop is one-half times mass times the radius of gyration.
Output (English): Science