While searching about equilibrium I came to this YouTube video which was quite astonishing but the video maker didn't explained the physics behind it. My query is that why the spoons aren't falling? The obvious answer that someone might give would be that they are in equilibrium, but why are they in equilibrium? I mean the mass is decreasing on one side, shouldn't it be unstable then? Also if the answers explaining this phenomenon in terms of forces will be much appreciated.
The part of toothpick which burns out in experiment is not important. "On the one side" we have part of spoon and part of fork, "on the other side" we have other parts of spoon and fork (handles). If you look on this system from above you will see, that the point toothpick touches glass is somewhere "inside" the system. If you draw a line through the touch point there will parts of spoon and fork both to the left and to the right of the line.
Center of mass of the whole object (fork, spoon and toothpick attached to each other) is somewhere near the point there toothpick touches the glass. A little lower (centimeter or two). Initial position is such that the center of mass is exactly below the point there toothpick touches glass. In this position the system is in stable equilibrium. The object can not fall by itself! If you push and tilt it a little the object will "rotate", by as it is rigid, the distance from the center of mass and the touch point will remain the same! So, the center of mass will be higher now. (The lowest possible position is when the center of mass is exactly under the touch point). So, the object can not tilt by itself - it needs a source of energy to lift it's center of mass. So, it remains in place.
Burning off the part of toothpick does not change the position of center of mass significantly. The toothpick doesn't burn completely because the glass absorbs heat and the toothpick doesn't burn near the point it touches glass.
You can easily repeat this experiment yourself. Try to tile the system a little by pushing some part of the object down. You will see that some other parts of the object will have to raise! The net effect would be that the center of mass will become higher - so the object can't tilt without external interaction. Tilting requires some energy!
The short answer is the location of the toothpick on the rim of the glass happens to be the location of the center of mass of the system which, in turn, happens to not be located at a point on the system itself. Since it’s the location of the center of mass, balance is achieved.
Hope this helps