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Newton's law of inertia applies: A body in motion tends to stay in motion, and a body at rest tends to stay at rest. This applies to earthquakes because a building or other large, fixed object is "at rest" and is not designed to be in motion. When the land vibrates and moves under a building due to an earthquake, the building has the contravening forces of inertia (the at-rest building tends to try to stay at rest) versus the ground under the building moving, and the ground doesn't play nice by moving smoothly and continuously in one direction. If it were not for inertia, the building and its contents (including people!) would simply move with the ground, and neither the building nor its contents would suffer damage.

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