Determining the centres of mass of a circular arc and a circular sector using the principle of virtual work

Abstract

In studying physics, it is important to solve problems with different methods and compare current and final results, which allows more comprehensive and deep analysis of the observed processes. In this paper, at a level of school physics course, the application of the principle of virtual work is presented as an alternative to the standard method for solving problems of statics. Two approaches are used to analyse two problems, as a result of which, without the use of integral calculus, formulas for the centres of mass of a circular arc and a circular sector are obtained.

Reply to comment on ‘Determining the centres of mass of a circular arc and a circular sector using the principle of virtual work’

“…We agree that our approach [1] for determining the centre of mass of the arc differs significantly from those proposed by Carlos Wörner [2,3]. The latter present both direct and two other interesting alternative approaches without relying on the use of the concept of mechanical energy.…”

“…In the approach to solving the problem [4] the increment of the potential energy of the body is calculated in two ways and the resulting expressions are * Author to whom any correspondence should be addressed. equated, but in our approach [1] the virtual work of the force holding the body in a state of equilibrium are equated to a change of the potential energy, and then the torque equilibrium is applied. The approach presented by Alexei Chernoutsan in a way is simpler than ours.…”

Example activity: how to determine the center of mass of a body if the center of mass is outside the body?

“…However, these sample applications for both moving and stationary bodies were structured for cases where the CM is inside the body. There are also examples where CM is outside the body, but these examples do not include applications and are based on theoretical calculations [9]. This study's aim is to present an activity for students to experimentally determine the location of the CM of bodies with a CM outside the body.…”