Falling beads on a falling rod

Abstract

The falling rod paradox, i.e. the fact that the tip of an almost horizontal rod falls with an acceleration ‘higher than g’, when the other end is hinged or supported, is a popular physics demonstration. It can be visualized by placing e.g. a coin on the tip of the rod and fixing a cup next to the coin. When the rod is released the free-falling coin is left behind and, if the vertical projection of its position is well aimed, the coin ends up in the cup. In this work we aim at visualizing the falling-rod paradox using a high speed camera and experimentally determine the point on the rod where the acceleration for various setups. To enhance the visualization we use evenly spaced beads on top of the rod. The experiments can be performed by pupils in the upper secondary school. Theoretical understanding may require first-year university classes in mechanics.