In this article, a 3D dynamic model and nonlinear free vibration analysis of a uniform beam attached to a rigid hub rotating at two adjacent rotary joints are presented. The nonlinear model is performed by considering the effects of steady-state axial deformation, Coriolis terms, and geometric nonlinearity by means of von Karman’s strain–displacement relations. The coupled axial, chordwise, and flapwise equations of motion are derived from Hamilton’s principle. Then, Galerkin’s procedure is utilized to discretize the governed partial differential equations. The effects of hub radius and rotational speeds are incorporated into the governing equations of motion. The relative effects of the Coriolis term on the flapwise and chordwise deformations of a considered 3D rotating beam are investigated. The validity of the present numerical results is verified by comparing them with the available results of the cantilever beam with and without the hub radius at various rotational speeds. The quantitative data obtained within the limit of speed of rotation reveals that the Coriolis factor has a significant impact on the flapwise bending frequencies but not really on the chordwise bending frequencies.