# Resemblance between Coriolis force and magnetic part of Lorentz force

If we interchange velocity with charge and omega that is rotation of a system with $B$, magnetic field, we get the same thing. Is there any deeper meaning to this same mathematical form?

From a mathematical point of view the two formulae $2m\mathbf v\times\boldsymbol\omega$ and $q\mathbf v\times\mathbf B$ have deep analogies. Both $\boldsymbol\omega$ and $\mathbf B$ are not vectors, but rather pseudo-vector (this notion stems from the fact that these two objects don't change under parity, contrary to a genuine vector). More precisely I'd say that they are 2-forms that can be represented as "vectors" because of the Hodge duality between $\bigwedge^2 V$ and $V$, where $V$ is a Euclidean space of dimension 3 (here I'm also identifying $V$ with its dual $V^*$).