Supercritical bifurcation of a spinning hoop
Résumé
The motion of a hoop hung on a spinning string provides an illustrative and pedagogical example of a supercritical bifurcation. Above a certain angular velocity threshold Ωc, the hoop rises and spins about its symmetry axis. The equation of motion is derived in the limit of a long massless string, and the calculated steady states are compared to experimental measurements. This simple experiment is suitable for classroom demonstration, and provides an interesting alternative to the classical experiment of a bead sliding on a rotating hoop.
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