Versatile Physical Pendulum

Abstract

It makes good sense to extend the range of usefulness of a piece of equipment beyond that intended originally. A commonly available “variable g” physical pendulum1 allows one to vary the angle α of its plane of oscillation to the vertical, so that in the expression for its period, g cos α replaces g. As shown in Fig. 1, the physical pendulum consists of a heavy cylindrical steel bob that can slide up and down a light aluminum rod whose top is attached to a cylindrical pivot resting on ball bearings. The aim of this paper is to describe a sequence of activities in rigid-body dynamics based on a triply modified version of this pendulum, extending over two lab sessions, carried out toward the end of a calculus-based mechanics course. However, the experiment can be analyzed at various levels, whether calculus based or by more elementary means. Figure 1 shows how we bolted a protractor to the top front of the instrument, so that one can measure the initial amplitude θ0 from which the bob is released. This enables one to study the amplitude dependence of the period between 0–90°. In addition, we have turned on the lathe an aluminum bob of identical shape and size. For this much lighter bob, the aluminum rod contributes a significant fraction to the total moment of inertia of the pendulum. Finally, we have improved the pivot's ball bearings, so that when released from 90° the pendulum continues swinging for 20 minutes or more, enabling one to observe the decay of its amplitude over a long time.