These two children were talking, and one boy was assuring the girl that his big ball would fall faster than her ball, which was smaller. When I heard this, I was naturally amused, and laughed.
The boy leaned over and whispered (children fashion),"Wait, till I do it, then he'll laugh on the other side of his face."
So, what does "laughing on the other side of your face" mean?
There's an interesting post about it here. Possible origins he mentions are head of Janus (a Roman mythological figure with two faces on either side of his head), or the tragic/Comic masks originating from Greek theatre.
The normal idiom is "laughing out of the other side of your face", not "...on..." (in the US, anyway). And according to Phrasefinder.org, it means basically that you will be dismayed when things don't go as you expect.
What I believe this idiom means is that it is similar to the idiom of "turning tables".
When someone will laugh the other side of his face can be given in a very simple example.
When a Nazi stormtrooper comes through the door you will laugh the other side of your face.
It means when you mock someone with laughter you might not find it too funny anymore after something happens.
