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As many as you like. Coordinate systems are arbitrary frameworks used to describe the system configuration (arrangement). The popular coordinate systems are rectangular, polar and spherical.

Coordinate systems are not the same as dimensions. A physical problem may have only one dimension and can be described in a three dimensional rectangular coordinate system. Physics since Einstein is believed to be 4 dimensional. A 4 dimensional coordinate system like quaternions would seem to be convenient.

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Q: How many coordinate systems are there in Physics?
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