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Centripetal force is the correct principle associated with the development of a rollercoaster ride because it describes the force required to make an object follow a curved path. In the context of a rollercoaster, as the train moves along the tracks, especially during loops and turns, centripetal force acts toward the center of the curve, enabling the car to maintain its trajectory without falling off. The design of rollercoasters takes advantage of this principle to ensure that riders experience thrilling turns and loops safely.

The other concepts mentioned, such as specific gravity, quantum energy, and the uncertainty principle, are not directly related to the dynamics of rollercoaster physics. Specific gravity deals with the ratio of a substance's density compared to water and does not play a role in the movement of a rollercoaster. Quantum energy pertains to the behavior of energy at a subatomic level, which is unrelated to macroscopic phenomena like rollercoasters. The uncertainty principle, a principle of quantum mechanics, describes limits in measuring certain pairs of physical properties, which again is largely irrelevant in the practical design and operation of rollercoasters. Thus, centripetal force is the key principle that governs the safe and exhilarating experience of rollercoaster rides.