Remember seesaws? Those things were great. But there was often a problem.
Suppose there’s a big kid on one side and a smaller kid on the other side. The seesaw just stays in one position: big kid on the ground, smaller kid up in the air. No fun. After a few different tries, you probably realized that moving the big kid in toward the center made it possible to rock a little. Move the big kid even more and you can achieve balance. Now the seesaw works.
What’s going on here? The answer is in the “center of mass.” The center of mass is a point somewhere along the plank that holds the two kids where their average weight falls. If you can get the center of mass to be over the pivot point, the seesaw will be balanced.
There’s a simple way to figure out where the center of mass is. If the big kid is two times as heavy as the little kid, then their mutual center of mass will be two times closer to the big kid than to the little kid. Three times heavier and the center of mass will be three times closer. And so on.
So the reason the heavy kid sits on the ground while the light kid is up in the air is that their mutual center of mass is on the heavy kid’s side of the pivot. To make the seesaw work, the heavy kid must push that center of mass forward until it just touches the pivot. Then their average weight pushes right on the middle, letting the ends rock up and down.