Supercritical bifurcation of a hula hoop
  The motion of a hoop hung on a spinning wire provides an illustrative and pedagogical example of a supercritical bifurcation. Above a certain angular velocity threshold Omega_c, the hoop rises, making an angle theta = (Omega-Omega_c)^(1/2) with the vertical. The equation of motion is derived in the limit of a long massless wire, 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 the bead sliding on a rotation hoop. 
Frederic Moisy