In this paper, the dynamics and trajectory of a rigid sphere in an annular groove rotating around a vertical axis is studied. The rotation and revolution of the sphere are coupled with each other through friction. Theoretically, the balance position of the sphere which monotonically increases with the rotating speed of the annular groove is obtained. And the damped oscillation of the sphere is solved numerically. In addition, an experimental setup is built with the help of 3D printing, and a method is proposed for measuring friction coefficient between the arc surface and the object thereon. The theoretical predictions are quantitatively verified by the experimental results.