Physics behind a match performing a trick on center of mass https://www.youtube.com/watch?v=Ucdw0DDI4n8
I've seen another variation where the whole match stick turned to ash.
What's going on in this trick?
 A: This is really two tricks in one. Let's look at each one individually.
The forks/cork/match set is balancing while being mostly not on top of the cup.
This has entirely to do with the center of mass for those objects. The center of mass for those four items appears to be on the lip of the cup. This is why, when the presenter pushes down on it, it "wobbles" and then goes back to balancing.
To understand more of what is going on, you can try looking at the system from the side. If the cork is on the leftmost part of what we can see, and the fork-grips are on the rightmost part of what we can see, you can start drawing some arrows representing the forces and torques on the system. The "balance point" is where the match meets the glass. If the torque on the left side of the balance point is equal to the torque on the right side, then the whole system will stay up. Effectively, the fork-grips are stopping the rest of the things from falling.
You can do this process with anything hanging off an edge; try it with a book! If you make diagrams showing the center-of-mass and the torques on each object, you may notice they look very similar. The fun part of the forks/corks/match is that you may not expect it on a single match stick. Speaking of which...
The match being lit on fire
This is appears just to be simple showmanship. (Fire! Pretty!) If the match-stick can support the weight of the forks/cork/match combination, it'll stay up. Turning the match-stick into ash simply degrades the structural integrity of the match. It may also change the weight distribution of the forks/cork/match combination, but not by much, so it stays up.
So, simple analysis of weight distribution and torque lets us do this sort of things.
