# Coriolis force - Question about sign

Dear all

I have a question concerning the Coriolis acceleration expression. I learnt it as Ac = -2ω x v, where ω is the vector which indicates the rotation axis direction of Earth and v the velocity of a body that I want to check the Coriolis effect on.

My question: where the minus sign comes from? As far as I understand, it depends on what reference frame I use (inertial or non inertial - the minus comes from the latter, like the Earth, in my conception). Am I correct?

Thanks in advance!

## Answers and Replies

A.T.
Science Advisor
Dear all

I have a question concerning the Coriolis acceleration expression. I learnt it as Ac = -2ω x v, where ω is the vector which indicates the rotation axis direction of Earth and v the velocity of a body that I want to check the Coriolis effect on.

My question: where the minus sign comes from?
You can swap ω and v, and the minus sign is gone:

-2ω x v = 2v x ω

As far as I understand, it depends on what reference frame I use (inertial or non inertial
The Coriolis force exist only in non inertial frames.

AlephZero
Science Advisor
Homework Helper
The minus sign is there because humans made the arbitrary decision to use right-handed coordinate systems rather than left handed ones.

The Coriolis force is just a consequece of Newton's laws of motion. The physics doesn't depend on what frame you use to describe it, or whether the frame is inertial or non-inertial. The details of the math depend on those things, but "the map is not the country", and similarly "the math is not the phyiscs".

tiny-tim
Science Advisor
Homework Helper
The minus sign is there because humans made the arbitrary decision to use right-handed coordinate systems rather than left handed ones.

no, it would still be there, because you'd still need v = ω x r

(btw, this is a duplicate thread to https://www.physicsforums.com/showthread.php?t=659387)

A.T.
Science Advisor
The minus sign is there because humans made the arbitrary decision to use right-handed coordinate systems rather than left handed ones.
To me it seems more like it's the arbitrary decision to have ω first in the term.