Abstract: This paper investigates the rigidity of rotating reference frames and discusses the motion of particles within such frames. Starting from Born’s relativistic rigidity condition, it is proven that the prerequisite for Einstein’s rotating disk to satisfy the rigidity condition is that the disk undergoes uniform rotation. Within a uniformly rotating reference frame, the geodesic equations of particles are analyzed, revealing the existence of forbidden regions related to constants of motion in the particle trajectories. For nonuniformly rotating reference frames, particle geodesics under different rotation functions are analyzed by defining an energy constant. The equations of motion for particles in both uniformly and nonuniformly rotating frames are analyzed, establishing the relationship between accelerations measured in the rotating frame and the laboratory rest frame. It is found that this relationship corresponds to the classical mechanical counterpart under the lowvelocity approximation. The discussions in this paper can further deepen the understanding of issues concerning the rigidity of rotating frames and the motion of particles within them.

Key words: rotating reference frame, Born’s rigid condition, geodesic