Depend, hinge, hang, turn are comparable when they mean to rest or, especially, to be contingent upon something uncertain or variable or indeterminable. All are normally followed by on or upon.
Depend, which literally means to hang or be suspended, suggests an element of mental suspense which makes forecasting impossible.
It often suggests uncertainty of a thing with reference to circumstances yet to take place, facts not yet known, or a decision yet to be made.
It may suggest also a variability that rests upon a difference in attitude or point of view.
Hinge is sometimes used interchangeably with depend; it may retain much of its literal suggestion of a movable part (as a door or a gate) that opens or closes upon hinges and then usually implies the cardinal (see under ESSENTIAL 2) point upon which a decision, a controversy, or an outcome ultimately rests.
In such use it suggests not so much mental suspense as uncertainty tempered by the certainty that the matter will go one way or the other.
Hang likewise may interchange with depend, but more precisely it suggests a point of support such as is characteristic of the literal action of hanging; the term therefore stresses not so much the uncertainty of the event as the weakness or the strength of what gives validity, authority, or credibility to something (as a doctrine, a belief, or a course of action) or of what points the way to fulfillment or successful performance.
Turn often comes close to hinge in its meaning. It as often differs from hinge in suggesting a rotation or pivoting rather than a going one way or the other and, therefore, in implying a dependence upon something that may be variable or casual.