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schrodingerwitch

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But we know that the frictional force must act against the direction of the object's movement, so its unit vector must have direction î (unitary).

Is this change in the unit vector simply a convention that comes from agreement with experimental physics or is there some kind of vector transformation that makes this vector j^ already become a vector î?

The books I researched were Halliday, Tipler, Moysés and Young and Freedman. In none of them did I see comments about it, so I think it might be trivial, but I wanted to clear that doubt. The only book that talked about it was Alonso and Finn - A University Course, but it was just a comment and I found it confusing.