The simple textbook problem of a particle on a vertical, rotating hoop is analysed both in theory and through exper-iments. We begin by detailing out a somewhat generalised theory, where the eﬀect of dry friction as well as the possibility of a shift in the vertical axis of rotation are incorporated. The bifurcation curves (plots of the angular position of stability versus the angular frequency of rotation) are obtained for all cases (i.e. with and without friction and a shift of the axis). Thereafter we present the experimental set-up fabricated by us and elaborate on the various measurements performed. Finally, we demonstrate through our experiments how well the theoretical results on the bifurcation curves tally with the experimental ﬁndings. The match between theory and experiment is found to be reasonably satisfactory. We conclude by mentioning how various aspects of this simple problem as well as its generalisations and extensions, are linked with dif-ferent advanced areas of physics.
Volume 26 | Issue 10