Republic of Singapore
World Scientific Publishing Company
The physics of a bead rolling on a roating hoop – a problem in nonlinear dynamics
Imagine a grooved hoop rotating about its vertical diameter. If you place a bead on the bottom of the hoop, the bead remains at the bottom, and will only rise up along the side if the angular velocity of the hoop exceeds a critical value. This is an example of a phase transition – upon a small increase in angular velocity at the critical value, the bottom of the hoop suddenly goes from being stable to being unstable, causing the bead to no longer stay there, and a new stable equilibrium is created on each side of the hoop. The physics behind this transition is quite general and can be extended to other systems, making this system a useful illustration of phase transitions. However, it has rarely been experimentally verified, nor is the motion of the bead approaching equilibrium investigated. My project develops a theoretical model including real-life conditions like rolling and damping, to predict the motion of the bead. I then experimentally verified the phase transition and motion of the bead, observed some interesting behaviours such as critical slowing down, and found how different parameters affect the system, gaining a better understanding of this classical problem.