Here's the list of fictitious forces that we learned about:
- Translational Force: In a frame translationally accelerating at $\mathbf a$, there is a fictitious force $$\mathbf F_{\text{trans}} = -m\mathbf a.$$
- Centrifugal Force: In a rotating frame, objects experience a radially outward fictitious force of magnitude $$\mathbf F_{\text{cen}} = m\omega^2 \mathbf r.$$
- Coriolis Force: In a rotating frame, objects which are moving are subject to the Coriolis force:
$$\mathbf F_{\text{cor}} = -2m\mathbf \omega \times \mathbf v.$$
- Azimuthal Force: In a rotating frame with non-constant angular velocity, the azimuthal force is $$\mathbf F_{\text{cor}} = -m\dot \omega \times \mathbf r.$$
An application of fictitious forces is tidal forces.
Idea: Tidal Forces
Due to the non-uniform force of gravity, a non-point mass experiences stretching and squishing forces. If there is a mass $m$ at $(R,0)$, then the tidal force on a mass $m$ is
$$\mathbf F_{\text{tidal}} = \frac{GMm}{R^3}(2x,-y).$$
This is simply derived from taking the reference frame of a mass at $(0,0)$ and then using binomial expansion.