Consider a simple wooden pencil resting on a smooth desk surface. Its full length lies flat, supported entirely by the wood beneath. Gravity pulls downward evenly, and the pencil remains perfectly still.
The pencil edges nearer to the desk's side. An increasing length overhangs into empty space, yet it stays balanced as long as its center of gravity rests above the solid surface.
The threshold crosses at the exact point when the pencil's center of gravity shifts beyond the desk's boundary. Support vanishes from under the midpoint.
Immediately before, the pencil holds steady in place. Immediately after, it pivots abruptly, one end dropping as the whole object accelerates toward the floor below.
The situation has changed: no longer perched securely, the pencil now follows the pull of gravity in descent.