The mechanical system "Rotating disk or cylinder" is considered under intensive loads, which differ from the steady-state process. The solutions tothe equations of the theory of elasticity for a steady-state process are only part of the solution of the problem, because after some change of the system in time the angular velocities do not cease instantly. The mechanical system under consideration is under the influence of various variables and impulse processes. Therefore, in the proposed article, the behavior of the considered mechanical system, in particular a rotating disk of constant thickness or a cylinder of finite length with a pulsed load, which is different from the steady-state process, was checked. The assumption of a slow change in time of the volumetric centrifugal force and heat flux, which appears under the action of an external load, leads to the consideration of motion as a certain sequence of the equilibrium state. Such an approach to solving problems of the dynamic theory of elasticity is called quasistatic. In quasistatic analysis of unsteady stresses, time is a parameter and therefore solutions for the corresponding stationary problems can be used. It is shown that transient processes cause the appearance of thermal effects that arise under the action of external loads. The action of external loads leads to the appearance of deformation and a change in temperature in the body under investigation. Any deformation, including elastic, is accompanied by thermal effects and therefore an attempt to describe the behavior of a continuous medium only by a mechanical scheme, ignoring the thermomechanical interaction inside the medium is difficult. Thus, during the deformation, the temperature of the body point changes, and as a result, absorption or release of heat by an elastic isolated body can occur, as it interacts with the surrounding medium. If the deformation of the body is small, then upon termination of the action of the volume forces that cause deformation, the body (cylinder or disk) returns to the initial undeformed state. The deformation process is very slow, that is, it will be thermodynamically reversible. The solutions given are obtained taking into account the differential equation of heat conduction of a hyperbolic type that does not admit an infinite velocity of propagation of temperature perturbations, in contrast to the differential equation of heat conductivity of a parabolic Fourier type. The differential equations of rotation of a rigid body around a fixed axis are solved. It is shown that the equation of motion and the heat equation are indirectly related. Formulas of stresses for rotating disks or cylinders in transient processes are obtained for the first time and are of great importance for the solution of many practical problems.