# Negative sign on Coriolis acceleration not necessary?

Why is the Coriolis acceleration often written as $$-2({\bf \Omega \times v})$$, (for example Wikipedia)? Why is it not written $$2({\bf v \times \Omega)}$$ which means the negative sign is not needed? For example, the Lorentz force on a charge moving in a magnetic field is not written as $${\bf F} = - q({\bf B \times v}).$$

• To-may-to, to-mah-to...
– Puk
Apr 10, 2022 at 19:07

The Coriolis acceleration is the Coriolis force divided by the mass. It has the negative sign because the Coriolis force appears as an additional force to the real forces to describe the acceleration in the non-inertial frame: $$(1) \enspace m{d^{*2}\vec r \over dt^2} = \vec F -2m\vec \Omega \times {d^*\vec r \over dt}$$ The starred time derivatives are with respect to the non-inertial frame. The left side of (1) gives the motion in the non-inertial frame; that is, the acceleration in the non-inertial frame. The right side of (1) includes all the forces that dictate this motion in the non-inertial frame: both the net external force $$\vec F$$ and the fictitious Coriolis force. Since the Coriolis force has the negative sign, so does the Coriolis acceleration.
The Lorentz force is a real force and as such is part of $$\vec F$$ when it is present.