Connection between gravitational and inertial masses of compound objects and the weak equivalence principle

The connection between gravitational and inertial masses of compound objects (e.g. nucleons, nuclei, atoms, and molecules) in the presence of rapid internal motions of their constituent parts is considered. The equality of gravitational and inertial masses of such objects confirming the weak equivalence principle is proven provided that their moving constituent parts are confined. The result is very nontrivial because of a substantial difference between particle dynamics in noninertial frames and gravitational fields. Paradoxically, gravitational effects are different for the same particles moving in the closed box and in the free space. The gravitational and inertial masses are equal to the corresponding kinematic masses. In contrast, gravitational masses of ensembles of noninteracting moving particles cannot be introduced because the total gravitational forces acting on these ensembles do not correspond to their kinematic masses.