The physical nature of rotational motion of material bodies is uncovered. When a classical particle moves on a curvilinear trajectory by inertia, an interaction of the particle with surrounding space is generated. As a consequence, the particle turns to an open non-local system occupying the whole space: it consists of an area of basic localization the linear dimensions of which are determined by the radius of curvature of particle trajectory, and a tail extending from the area of basic localization to infinity. There are quantum states of classical particle, representing a superposition of states of the classical particle and its images - virtual particles. The particle and its images are bound together by a power cord to form a stable spatial structure, which is similar to the excited states of quantum particle considered in standard quantum mechanics. Thus, we come to the quantum picture of motion of classical particles. The physical mechanism of interaction between classical particle and space lies in the fact that when the particle moves on a curvilinear trajectory by inertia, a specific physical medium - a vortex vacuum medium (VVM) having quantum structure is generated. It is important to note that the VVM is not introduced into theory as a hypothetical medium, which is arbitrarily endowed with some physical properties to suit the researcher; it appears with necessity as a consequence of the curvilinear particle motion by inertia and all its properties are defined by this motion. The particle is enveloped by a cloud of virtual particles forming the quantized VVM. The interaction of particle with the surrounding space is carried out through the exchange of the energy and momentum quanta between the particle and the VVM. The physical characteristics of elementary excitations of the VVM (VVM excitations) are defined. The region of the energy spectrum of the VVM excitations corresponding to the processes of transformation of classical particles in the VVM and to the reverse process - the transformation of the VVM in ordinary matter is found. In the energy spectrum of VVM excitations, there is a critical point at which the complete transformation of the classical particle in the VVM takes place. The dematerialization of classical particle does not at all mean that the matter disappears. It represents the conversion of ordinary matter in the latent (hidden) state - a VVM matter. The processes of materialization of VVM and dematerialization of matter are natural analogues and generalizations of the quantumelectrodynamical processes of annihilation of particle-antiparticle pairs with the formation of photons and the reverse processes -