Experimental analysis of a compound pendulum with variable suspension point

Abstract

A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is measured using three different methods: a smartphone used both as an independent tool or as a data-logger and commercial photo-gate. The experimental results are successfully compared with theoretical calculations based on the addition of inertia moments and the Steiner theorem.

Measuring the moment-of-inertia of a rigid body using a swing-pendulum

“…In this way, one may infer the body's moment-ofinertia I empirically by measuring the pendulum's time-period T for a given h [6,7]. Almost all textbook analyses of the compound pendulum use a pivot O internal to the body (see figure 1(a)) [5], and it is therefore no surprise that experiments reported in the wider literature typically do the same, either by forcing a pivot through the body, or by boring a hole as a point of suspension [6][7][8][9][10][11]. Such approaches are effective if the rigid body is relatively small, and made from a low-friction material that can be worked easily; however, if the body is impractically large or heavy, or if damage by boring is to be avoided, then fashioning an internal pivot is more difficult.…”

Teaching the moment of inertia by measuring the angular speed with a smartphone’s sensors

“…Currently, most experiments for studying the moment of inertia use a torsion pendulum or physical pendulum. For example, Monteiro et al used the gyroscope sensor with appropriate applications (apps), such as the Phyphox app and the Androsensor app, to measure the oscillation period for the analysis of a compound pendulum with a variable suspension point [1]. The period of the physical pendulum depends on its moment of inertia or the position of the suspension point.…”