An attention-grabbing center-of-mass demonstration uses the map of a state mounted on a sheet of heavy cardboard and cut out along the boundaries. The two-dimensional object is hung from a hole punched into a city near the edge, and a string with a pendulum bob attached to it passes through the center of mass. The process is repeated with a different city, and the center of mass is determined uniquely. I did this regularly with a map of the state of Ohio, and the geographic center of the state reliably came out to be the nearby village of Centerburg.