How to find the center of gravity of a flat piece of card (lamina) ?
Use the pin to hang your lamina and your string on your stand. Then draw a line on your lamina along your string. Hang the lamina from a different point and repeat. Where the two lines intersect should be the center of gravity. Why does this work? In order for the lamina to be in a stable equilibrium, torque about the pin needs to be zero. The torque becomes zero when your center of gravity is directly under the pivot. The string just helps you draw a straight line down. The center of gravity must be on that line, but you don’t know where on that line. Then you draw a second line from a second pivot. The center of gravity must then be on both lines, and the only way for a point to be on two lines at the same time is if the point is where those lines exist. NOTE: This fails when the center of gravity is outside the lamina because you can’t draw a line there. You can, however, imagine a line to give you a rough idea where the center of gravity is.
