Measuring the inertial mass using a Roman balance

Abstract

We describe a simple teaching laboratory device for measuring inertial mass based on the quasi-static equilibrium of a Roman (steelyard) balance on a horizontal plane, suppressing the influence of gravity. This device offers an alternative operational definition of inertial mass. Compared to traditional definitions based on measurements of acceleration (such as the classical definition by Ernst Mach) or of the frequency of a mass-spring system, this method does not require measurements of time, acceleration, or force; uses a simple and cheap apparatus; and yields the correct value even if performed in a non-inertial frame, or by an observer in relativistic motion. The apparatus also allows measurement of the gravitational mass, and demonstrate its equivalence with inertial mass, in a simple and elegant fashion. For these reasons, the method is eminently suited to demonstrations and lab classes in introductory physics courses.

Keywords
mass; inertial mass; gravitational mass; Roman balance; physics laboratory