The surprising rolling spool: experiments and theory from mechanics to phase transitions

An asymmetric rolling spool can be investigated as a simple model for a second-order phase transition. At low energy it undergoes librational motion around the equilibrium position, whereas at high energies its motion becomes rototranslational. The analysis of its dynamics shows that when approaching critical energy, the period of oscillation diverges; and this suggests the transition from one phase to the other. We thus show that the concept of ‘phase transition’, useful to describe the behaviour of a variety of thermodynamic systems, can be actualized in this simple mechanical system. Moreover, a tight analogy can be found between the rolling spool’s behaviour and the Tomlinson model of sliding friction. This analogy makes it possible to interpret the critical switch of static friction near the threshold of motion as a phase transition. The rolling spool can be easily constructed and used as a hands-on experiment. Quantitative measurements of its motion were carried out through open-source video analysis software.