# Position of Center of Mass example from Feynman's Lecture

While going through Feynman's Lectures on Physics, I came across this paragraph(from the chapter Rotation in Two Dimensions) that got me confused:

So if we have some kind of a box, perhaps a space ship, with people in it, and we calculate the location of the centre of mass and find it is standing still. The centre of mass will continue to stand still if no external forces are acting on the box. Of course, this spaceship may move a little in space because people are walking back and forth inside; when one walks toward the front, the ship goes towards the back to keep the average position of all the masses in the same place.

I cannot imagine the scenario in my head and the ship going backwards as one person moves to the front, is non-intuitive for me.

It would be great if you could explain this with a bit of mathematics or maybe with a more relatable example than a space ship.

## 2 Answers

A personal anecdote might help you. I went out with some friends on a small boat. When we returned, the boat was only about a foot from the quayside, so I decided to jump ashore. I was forgetting Newton's third law. When I went to leap over the gap, instead of my leg just propelling me forward, it propelled the boat away from the quayside too. I ended up in the air with no boat below me, and fell into the sea, much to the amusement of my friends.

When the people on the spaceship walk forward, they are also propelling the spaceship backward to some extent. The size of the effect on the ship's position depends upon the relative masses of the spaceship and the walkers.

Okay , so this a very common phenomena. There reason behind this , since there is no external force the spaceship and people as a system , the net position of center of mass remains same.

To understand why does ship moves backward , you should analyze the problem by making a free body diagram of the man and the ship and try to find how / why does the people move forward ?

And the answer to that is friction .

When the people move forward the friction pushes them forward and at the same time it pushes the spaceship backward direction (Newton's Third Law) , so that position of center of mass is fixed.

I hope this makes a little sense.