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A mass constrained to move on a rotating hoop is an excellent mechanical model of first- and second-order phase transitions. Although the minimum of the potential energy curve corresponds to the bottom of the hoop at low rotation frequency, a spontaneous symmetry breaking (cusp catastrophe) occurs as the frequency is increased. Although the equations governing these rotating hoop models can be understood using elementary mechanics, they can be used to illustrate advanced concepts such as symmetry breaking and phase transitions. The Dynamics on a Rotating Hoop model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_mech_lagrangian_RotatingOffAxisHoop.jar file to run the program if Java is installed.
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