Analysis of the normal force variation for a falling rod

Abstract This paper studies the classical well-known problem of the rod rotating about the bottom end pivoted with a hinge and sliding without friction. The analytical solutions for the normal force and velocity of the centre of mass (CM) depending on the angular displacement are obtained. The intuitional graphs of numerical solutions for the normal force and the motion of the CM with the angular displacement are presented. Accordingly, the normal forces of the fixed hinge and free sliding motion are compared and this in turn highlights the difference between constrained and unconstrained motion of a falling rod.