= Coriolis force does no work
{c}
{title2=$\mathbf F_{\rm cor}\cdot\mathbf v_{\rm rot}=0$}
The instantaneous <power> of the <Coriolis force>, evaluated with the <velocity> in the same <rotating reference frame>, vanishes:
$$
\mathbf F_{\rm cor}\cdot\mathbf v_{\rm rot}
=-2m(\boldsymbol\Omega\times\mathbf v_{\rm rot})\cdot\mathbf v_{\rm rot}=0.
$$
This follows from the perpendicularity of the <cross product> and the <dot product> definition of <power>. The <Coriolis force> alone does no <work> and cannot change the rotating-frame <kinetic energy> $m|\mathbf v_{\rm rot}|^2/2$. It can change the direction of the relative <velocity>. Actual <forces> and the <centrifugal force> can still change that <kinetic energy>, as the <free particle in rotating coordinates> illustrates. Conservation of an appropriate total <energy> has the additional conditions stated under <energy balance in a uniformly rotating frame>.
Back to article page
