Radius of Gyration of a Sphere and a Barrel

This paper describes a method for measuring the radius of gyration of a circular object. In the experiment a circular object rolls down an elevated incline and then falls freely to the ground. Its radius of gyration is determined by its initial height on the incline, as well as the height and range of the free fall. The determination relies on many basic concepts, such as rolling without slipping, relationship between translation and rotational kinetic energies, conservation of energy, and equations of motion for free fall. The method is applied to measure the radius of gyration of a sphere and a barrel. The apparatus is so simple that students can do the experiment at home.