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Supposing I am in a non-inertial system and I don't know what forces are acting. How can I test EXPERIMENTALLY and in practice to be in a non inertial system? If I am in a system and I don't know how does it moves and I would make an experiment to test if this is inertial or not, what should I do? For example: in a lift? In a rotating system?

Qmechanic
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Inertial frame of reference is such that free bodies move with constant velocity. If you detect free body accelerating, the frame is not inertial.