This paper addresses dynamics of the rotor, which is vertically secured in one immovable hinge and one elastic support. There were received and analyzed equations of dynamics for description of disk-shaped and cylindrical rotor with dynamic unbalance. From the overall system of equations, there was received a system of equations for description of dynamics of the rotor under the impact of only static unbalance or only moment unbalance. There were considered cases of stable rotation of the rotor. There were obtained and analyzed dependencies for definition of all forces and moments, which impact the rotor. There were defined conditions at which stability of the rotor's rotation is secured. Studies encompass basic operational modes of the rotor's rotation. Dynamics of the rotor is described by elementary algebraic equations.