= Coriolis force
{c}
{title2=$-2m\boldsymbol\Omega\times\mathbf v$}
{wiki}
The Coriolis force is the apparent <force> proportional to a particle's <velocity> relative to a <rotating reference frame>. For constant <angular velocity> $\boldsymbol\Omega$ and particle <mass> $m$,
$$
\mathbf F_{\rm cor}=-2m\boldsymbol\Omega\times\mathbf v_{\rm rot},
\qquad
\mathbf v_{\rm rot}=\left(\frac{d\mathbf r}{dt}\right)_{\rm rot}.
$$
Here $\mathbf v$ in the title formula means $\mathbf v_{\rm rot}$, not the <velocity> measured in an <inertial frame>. The <Coriolis force> belongs to the chosen <reference frame>: a particle stationary in that <rotating reference frame> has no <Coriolis force>, even though it can have a nonzero <velocity> in the laboratory. Other <reference frames> assign different <angular velocities> and relative <velocities>, and hence different <Coriolis forces> to the same motion.
The <cross product> makes the <Coriolis force> perpendicular to both $\boldsymbol\Omega$ and $\mathbf v_{\rm rot}$, with magnitude $2m\Omega|\mathbf v_{\rm rot}|\sin\alpha$, where $\alpha$ is the <angle> between them. Apply the <right-hand rule> to $\boldsymbol\Omega\times\mathbf v_{\rm rot}$ and then reverse its direction. Motion parallel to the rotation axis gives zero <Coriolis force>; reversing the relative <velocity> reverses the <Coriolis force>.
The appeal of this description is practical: axes attached to the <Earth> or a turning apparatus can be kept fixed on the page, provided <Newton's second law> includes the extra terms. A <free particle in rotating coordinates> shows exactly how a straight laboratory <trajectory> can become curved, while <Coriolis acceleration in local Earth coordinates> gives a useful terrestrial scale. The <rotating-table demonstration of Coriolis deflection> makes the two viewpoints visible in one experiment.
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