Past exam of the mathematics course of the University of Cambridge / 2013 / ia / Paper 4 / 11B / i / Solution

Write the position in the rotating basis as $\mathbf{r}={\sum }_i{x}_i^{\prime }{\mathbf{e}}_i^{\prime }$. Differentiating with respect to time in the inertial frame,Here ${\mathbf{v}}^{\prime }={\sum }_i{\dot{x}}_i^{\prime }{\mathbf{e}}_i^{\prime }$ is the relative velocity measured in the rotating reference frame. ConsequentlyThis is the vector differentiation rule for a rotating reference frame with a common origin: the extra term accounts for the changing basis, not a translational motion of that origin.