Bead on a uniformly rotating rod: why does the bead move out if there is no force in the radial direction?

Abstract

Abstract Problems involving rotating systems analysed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. In this article we try to see what could be the factors that lead to this difficulty and propose a set of arguments that could be used to resolve the confusion. We take a specific example of a bead sliding without friction on a rotating rod to address the issues involved. After solving the problem in the inertial reference frame by integrating the equations of motion expressed in the plane polar coordinate system, we carry out a consistency check on how the radial motion can be accounted for by the force that the rod exerts on the bead. We hope that going through this exercise would help students to get more comfortable with understanding problems in a similar mould.