Two experiments for the measurement of the centre of percussion of a physical pendulum

Abstract

In this article we describe two experiments, performed with instrumentation commonly available in undergraduate laboratories, to measure the position of the centre of percussion of a physical pendulum. The first one makes use of a constant external force provided by a common spring dynamometer, and allows for a straightforward analysis founded on basic concepts of rigid body dynamics. The second one is, more properly, an experiment based on a percussion, i.e. a collision involving an almost impulsive force, and displays the typical difficulties, but also the physical richness, of this type of phenomena. We provide an historical overview of the problem of the centre of percussion, starting from its first formulation given by Bernardino Baldi at the end of the 16th century, and we show how the mathematical model built for analysing the impact between a physical pendulum and a localised object is helpful in understanding that such a problem, in its original formulation, does not have a unique answer.

When experiment and energy conservation collide: video analysis of an unrolling mat

“…The uncertainty in e is found to be ±0.04 by varying its value to generate curves that bracket the range of variation in the data points. Given that the bamboo rods of the sushi mat are tumbling across an oak table, this value of e falls within the accepted range of 0.4-0.6 for the COR of wood on wood [11].…”

“…using equations (1) and (4). Substituting equations (8) through (11) into (7) gives the total kinetic energy of the rolling mat as…”