• Sayan Kar

      Articles written in Resonance – Journal of Science Education

    • An Introduction to the Raychaudhuri Equations

      Sayan Kar

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    • Physics of a Particle on a Rotating Hoop: Experiment and Theory

      Kushal Lodha Anushree Roy Sayan Kar

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      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.

    • Analog Raychaudhuri Equation in Mechanics

      Rajendra Prasad Bhatt Anushree Roy Sayan Kar

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      Usually, in mechanics, we obtain the trajectory of a particlein a given force field by solving Newton’s second law withchosen initial conditions. In contrast, through our work here,we first demonstrate how one may analyze the behaviour of asuitably defined family of trajectories of a given mechanicalsystem. Such an approach leads us to develop a mechanicsanalogue following the well-known Raychaudhuri equationlargely studied in Riemannian geometry and general relativity.The idea of geodesic focusing, which is more familiar toa relativist, appears to be analogous to the meeting of trajectoriesof a mechanical system within a finite time. Applyingour general results to the case of simple pendula, weobtain relevant quantitative consequences. Thereafter, weset up and perform a straightforward experiment based ona system with two pendula. The experimental results of thissystem are found to tally well with our proposed theoreticalmodel. In summary, the simple theory and the related experimentprovide us with a way to understand the essence of afairly involved concept in advanced physics from an elementarystandpoint.

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