In obtaining the instantaneous angular velocity of a rotating rigid body, a large number of standard textbooks uses an incorrect argument by only considering the rate of change of the Euler angles but disregarding the simultaneous rate of change of the corresponding time‐dependent rotation axes. Therefore, a correct and concise derivation of this quantity for a rather general case is given, which also reveals that the usual simple formula does not at all arise as the erroneous textbook reasoning suggests, but as a consequence of certain generalized commutation relations satisfied by Euler rotations.

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