If a frame rotates with angular velocity $\boldsymbol{\Omega}(t)$ and translates with acceleration $\mathbf{A}(t)$, the observed acceleration differs from the inertial one by terms involving $\mathbf{A}$, $\boldsymbol{\Omega}\times\mathbf{v}$, and $\boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r})$.

In a rotating frame, one writes $m\mathbf{a}'=\mathbf{F}+\mathbf{F}_{\mathrm{fict}}$, where $$\mathbf{F}_{\mathrm{fict}}=-m\mathbf{A}-2m\boldsymbol{\Omega}\times\mathbf{v}'-m\boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r})-m\dot{\boldsymbol{\Omega}}\times\mathbf{r}.$$ These are, respectively, translational, Coriolis, centrifugal, and Euler forces.

Rotating-frame mechanics explains weather-system deflection, Foucault pendulum precession, and dynamics in turntables and spinning spacecraft. The Coriolis term is especially important in geophysical flows and precision experiments.