= Solution
Let a frame's origin have inertial acceleration $\mathbf a_0$ and its axes rotate with <angular velocity> $\boldsymbol\Omega(t)$. For position $\mathbf r$ and <velocity> $\mathbf v'$ measured in that frame, Newton's law becomes
$$
m\mathbf a'=\mathbf F-m\mathbf a_0
-2m\boldsymbol\Omega\times\mathbf v'
-m\dot{\boldsymbol\Omega}\times\mathbf r
-m\boldsymbol\Omega\times(\boldsymbol\Omega\times\mathbf r).
$$
The extra terms are translational, Coriolis, Euler and centrifugal inertial <forces>. <Centrifugal force> points away from the rotation axis; <Coriolis force> deflects moving bodies sideways and does no instantaneous <work> on their relative motion, since it is perpendicular to $\mathbf v'$. The Euler term appears when the rotation rate or axis changes.
For constant $\boldsymbol\Omega$, <centrifugal force> has potential $U_{\rm cf}=-m|\boldsymbol\Omega\times\mathbf r|^2/2$. It can be combined with a conservative real potential to find rotating-frame equilibria. The Coriolis term remains <velocity> dependent. These <forces> arise from describing acceleration in a noninertial frame; they are not additional interactions between bodies. They are essential for trajectories on rotating apparatus and for large-scale terrestrial motions. \b[Frame-dependent terms must be included consistently with the chosen coordinates.]
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