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.
Please note that this resource requires
at least version 1.5 of Java (JRE).
Rotating On Axis Hoop
A simplified version of the off-axis Dynamics on a Rotating Hoop model. download 1685kb .jar
Last Modified: January 19, 2012
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Dynamics on a Rotating Hoop Source Code
The source code zip archive contains an XML representation of off-axis and on-axis Dynamics on a Rotating Hoop models. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 59kb .zip
Last Modified: September 2, 2009
W. Christian, Computer Program DYNAMICS OF A BEAD ON A ROTATING HOOP MODEL (2008), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667).
W. Christian, Computer Program DYNAMICS OF A BEAD ON A ROTATING HOOP MODEL (2008), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667>.
Christian, W. (2008). Dynamics of a Bead on a Rotating Hoop Model [Computer software]. Retrieved May 27, 2022, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667
Christian, Wolfgang. "Dynamics of a Bead on a Rotating Hoop Model." https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667 (accessed 27 May 2022).
Christian, Wolfgang. Dynamics of a Bead on a Rotating Hoop Model. Computer software. 2008. Java (JRE) 1.5. 27 May 2022 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667>.
%A Wolfgang Christian %T Dynamics of a Bead on a Rotating Hoop Model %D 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667 %O application/java
%0 Computer Program %A Christian, Wolfgang %D 2008 %T Dynamics of a Bead on a Rotating Hoop Model %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7890&DocID=667
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The Dynamics of a Bead on a Rotating Hoop Model involves the notion of two reference frames, supplementing the material covered in Physlet Physics chapter 9.
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