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A pendulum without a supporting string or rod is obtained if a small block or marble is released at the rim of a spherical bowl or cylindrical half-pipe. This setup also applies to the familiar loop-the-loop demonstration. However, the bob will then experience sliding or rolling friction, which is speed independent in contrast to the linear or quadratic air drag which is more commonly used to model damping of oscillators. An analytic solution can be found for the speed of the bob as a function of its angular position around the vertical circular trajectory. A numerical solution for the time that the object takes to move from one turning point to the next shows that it is smaller than it would be in the absence of friction.

Recently, the use of video analysis technique has emerged as an effective and facile learning tool, due to the richness of spatial and temporal data useful to investigate the complex physical phenomena related to kinematics. In this study, we have investigated the motion of solid and annular cylinders rolling down an inclined wooden plane at different angles. The linear accelerations of the cylinders for the case of rolling (with and without slipping) have been derived theoretically and have been compared with their experimental counterparts. Specifically, the experimental values have been determined by performing a series of experiments, wherein the motion of the cylinders has been captured via a digital camera (recording at 240 frames s${}^{-1}$) and later analyzed frame by frame utilizing in-house developed GUI-based “Phystrack” video tracking library. We have measured the transition angles corresponding to the transition of motion (a) from rest to rolling, and (b) from pure rolling to a combination of rolling and slipping mode of motion, for the case of two distinct cylinders. This has eventually allowed us to compute the coefficient of static, kinetic and rolling friction for the aforementioned cylinders. In general, the coefficient of kinetic friction is regarded as an intrinsic material-dependent constant and considered as independent of the geometry of the object. However, in the case of rolling motion, the coefficients of friction are strongly dependent upon the geometrical parameters of the rolling object. The study emphasizes on developing the conceptual understanding ability of physics students pertaining to the friction coefficient of rolling objects.