Here’s the challenge. Start facing a wall while standing as close as possible. Now take two foot-sized steps back and put your feet together. Lean over so that your head rests against the wall (but keep your feet stationary). Next, pick up a chair and hold it near your chest. Ready? OK, stand up without moving your feet.
It’s a challenge because some people are able to do this move, but some can’t. Me? Oh, I can’t do it. Maybe you can. You should try it. Of course this involves physics, let’s look at the key ideas.
Center of Mass
Suppose you have a stick with a length L and mass m. If you drop this stick, it will obviously fall. We can treat this stick as just a point mass and it will move downward with an acceleration of -9.8 meters per second per second (a value of g). Since we are just considering this to be a point mass, the gravitational force is acting on the point. It’s simple.
Now imagine that the stick is on a table with part of the stick hanging over the edge of the edge. Maybe we want to find out when the stick will fall off or something. You can’t treat the stick as just a point mass because clearly the location of stuff matters. In particular, where does the gravitational interaction exert a force on the stick? The answer is everywhere. All parts of the stick have mass, so all parts have a gravitational force. But it turns out that all of these forces on all of these masses are the same as if one single gravitational force acted on the stick at a particular point. We call this point the center of mass (it’s technically the center of gravity, but it doesn’t matter in this case). For a simple stick, the center of mass is in the center of the stick.
What if the object isn’t so simple as a plain dumb stick (not really dumb, but sticks are dumb)? Let’s say that I have some “object” made of 3 different masses. Like this.