Why can’t you change seats on an empty plane?

This is the last one flight of the day and the plane is pretty empty. So you think, oh well, you’ll go up a few rows, where there’s a nice window seat with a view unobstructed by the wing.

Not so fast, buster. The flight attendant says this is unacceptable. You must remain in your assigned seat or you will disrupt the weight distribution of the aircraft. Really? Would a normal sized person moving make a difference? Yes, you know where this is going: Answering this question requires a bunch of awesome physics. So let’s get to it!

Mass Center

People often say that the center of mass of an object is where all the gravitational force acts. It’s a definition that works fairly well, and you can use it to solve many physics problems, but it’s not really true. In fact, gravity pulls all of them parts of an object, not just a point.

(A quick side note: We’ll actually watch center of gravitynot the center of mass, they are the same in a constant gravitational field as on Earth.)

If you really want to understand the center of mass, you have to think torque. If we look at Newton’s second law, it says that a net force changes the motion of an object (F_net = mass × acceleration). So if the net force is zero, the motion of the object will not change. If it moves at a certain speed, it will continue to do so. If it is at rest, it will continue to rest.

Here’s a little experiment: Place a pencil on a flat table and then take two index fingers and push it from the opposite side, right through the center. It just stays there, doesn’t it? Since you are applying equal and opposite forces, the net force is zero. But what if you push it like this:

Pencil pusherGraphics: Rhett Allain