Determination of earth's gravitational acceleration and moment of inertia of rigid body using physical pendulum experiments

Abstract

To determine the value of earth's gravitational acceleration, physical pendulum experiment is preferred over simple pendulum experiment that was previously more popular. In physical pendulum experiment, the object is a rigid body. The swing period and swing shaft position are measured. From these two variables and using the applicable laws of motion, equations can be determined that involve constants which imply the value of the earth's gravitational acceleration and the moment of inertia of objects pivoting at the center of mass. The independent variable in the equation is a function of the distance of the pendulum shaft to the center of mass based on the parallel-axis theorem, while the dependent variable is a swing period. Difficulty in solving equations is found because of the terms of the equation involving variables in different ranks. In order for the equation to be linear, a dependent variable and an independent variable are combined into new variables. After that, with the linear regression method, the constants of the equation can be determined which can then be determined the value of the earth's gravitational acceleration and the moment of inertia of the object. The results obtained are quite satisfactory with a relatively smaller error value of 5%. Thus this physical pendulum experiment can be used to determine the earth's gravitational acceleration and the moment of inertia of an object simultaneously.