FROM MULTIPLE SOLUTIONS TO COGNITIVE ADVANCEMENT: THE “MULTIPLE-SOLUTION” APPROACH TO CONSTRAINED MOTION ON A ROTATING CIRCLE

Taking the constrained motion of a particle on a rotating circular hoop as a case study, this paper systematically constructs and compares multiple solutions based on different reference frames, including inertial and non-inertial frames as well as translational and rotating frames, and different coordinate systems, including polar and natural coordinates, within the frameworks of Newtonian mechanics and analytical mechanics. The multiple-solution approach reveals the intrinsic relationships among transport motion, inertial forces, and relative motion. It also deepens students’ understanding of abstract concepts, promotes the systematic integration of classical mechanics, and facilitates the flexible transfer of problem-solving strategies. Furthermore, this approach integrates knowledge instruction with the cultivation of higher-order thinking, guiding students to move beyond mechanical formula application toward multi-perspective exploration, critical analysis, and active knowledge construction. Consequently, it helps develop students’ divergent thinking, critical thinking, and higher-order problem-solving abilities.