The Physical Pendulum: An Illustrative Teaching Laboratory Example Using a Long Rod

Here, a relatively simple laboratory experiment of a physical pendulum, suitable for students of science and engineering in the first courses of university physics, is presented to illustrate its dynamic behavior and to determine its inertia moment. To this end, a long wooden rod of length L = 99.8 cm and cross-section radius R = 1.73 cm was used as the physical pendulum. The period of oscillation was measured as a function of the distance from the rotation axis to the center of mass. It is shown that the oscillation period is a superposition of two contributions, namely, a linear and a hyperbolic function, which has a minimum at the distance [Formula: see text], where I0 is the moment of inertia of the rod about the rotation axis at its center of mass, and M is its mass. It is further shown that this quantity is independent of mass for all bodies of constant density, and a numerical method is applied to obtain the moment of inertia of the rod. Results obtained from a laboratory experiment agree with the expected one within 4%.