Tying a string to an object is a non-mathematical way to demonstrate the principle of the center of gravity. For oddly shaped objects, the center of gravity can be located by dangling the object from one spot, tracing the line of the string, and then hanging the object from another spot and tracing the line. The place where the lines intersect is the center of gravity.
Another way to demonstrate the center of gravity is to attempt to move someone when his center of gravity is not balanced. Let students try leaning over and grabbing their toes. Without moving their hands, ask them to try to hop forward. Because the center of gravity is over their heels, it is impossible to go forward, but they can hop backwards. Have students try to stand up from a chair while keeping their backs straight and arms crossed. The center of gravity is too far back to allow them to stand.
Paper airplanes will balance on fingertips or pencil points at their centers of gravity. Have students fold a paper airplanes and balance them on their fingertips. Mark those points on the planes. Ask students to change the centers of gravity by attaching small paperclips to spots on the airplanes. Find and mark the new centers of gravity. See if one configuration flies better than another.
Ask students to spin a basketball on their fingertips. Discuss why this works. Note that the balls spin around their centers of gravity. That axes are where the balls balance. Have students try to balance other sized balls and objects with other shapes on their fingertips. Have them record which ones are easiest to balance.