Now place a pork chop on one side of the plate. The center of the plate is no longer the center of mass. The pork chop side tilts downward, and pretty soon you have a mess on the kitchen floor and a happy dog.
Integral calculus can be used to find the center of mass of various objects in 2 or 3 dimensions, and even higher dimensions if you have a vivid imagination. Higher order integrals, called moments, are used to measure the energy of spinning objects.