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Physics

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    $\begingroup$ It’s not clear to me what your question is. If you’re saying that perhaps Morin phrased the argument only for the position vector but not other types of vectors, then my response is simply that you have to repeat the similar steps and see that the argument goes through in general. This formula is completely general, and holds for any vector-valued map. See here for the general formulation. $\endgroup$
    – peek-a-boo
    Commented Jan 1 at 13:41
  • $\begingroup$ If one has a velocity vector ${\vec v}^\prime$ in a non-inertial frame which has an origin with velocity, $\vec V$ with respect to some inertial frame; then in the inertial frame the velocity is given by:$\vec v=\vec V+\vec v^{\prime}$. Such reasoning follows from the ordinary notion of addition of vectors. $\endgroup$
    – Albertus Magnus
    Commented Jan 1 at 15:36
  • $\begingroup$ Although my above statement about vectors is true, it doesn't really help when one wants to determine an explicit form for the time derivative of a vector in a non-inertial frame. $\endgroup$
    – Albertus Magnus
    Commented Jan 1 at 15:56