hinge
A joint that lets a door or lid swing open.
A hinge is a joint that lets something swing open and closed while staying attached at one point. Most doors have hinges on one side: they connect the door to the frame so you can push the door open and pull it closed without the door falling off. Cabinet doors, laptop screens, and jewelry boxes all use hinges.
A hinge typically has two metal plates joined by a pin. One plate attaches to the door, the other to the frame. The pin lets them rotate smoothly. Without hinges, you'd have to completely remove a door every time you wanted to walk through it, then prop it back in place afterward.
The word also describes anything that serves as a crucial turning point. When historians say that a battle was the hinge of a war, they mean everything turned on that moment. One side's victory changed the entire direction of the conflict. If your science fair project hinges on whether your plant experiment works, the whole thing depends on that result. When something hinges on a particular factor, that factor determines what happens next, just like a door's movement depends entirely on its hinge.