Coriolis expression - Question about sign

[Curious2013]

Homework Statement

Dear all

I have a question concerning the Coriolis acceleration expression. I learned 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!

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Curious2013! Welcome to PF!

I have a question concerning the Coriolis acceleration expression. I learned 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?

There's no Coriolis force in an inertial frame.

(same as centrifugal force)

 

[TheEtherWind]

The sign is solely due to the choice of coordinates. Here's a site that derives it as positive:

http://www.nws.noaa.gov/om/wind/deriv.shtml

 

[tiny-tim]

Here's a site that derives it as positive:

no, it derives it as negative …

Coriolis force exists only in the Earth's frame (the rotating frame),

so in that frame (d²R/dt²)_Earth is on one side of the equation, and everything else on the other side …

the Coriolis force then does have a negative sign ​

 

[Nickie]

The minus sign in the Coriolis acceleration expression, Ac = -2ω x v, comes from the fact that the Coriolis effect is a result of the Earth's rotation, which introduces a fictitious acceleration in the non-inertial reference frame of the Earth. In this reference frame, objects appear to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is due to the fact that the Earth's rotation axis is perpendicular to the plane of motion, and the cross product between the Earth's rotation vector ω and the velocity vector v results in a minus sign. Therefore, the minus sign in the Coriolis acceleration expression is necessary to account for the direction of the Coriolis effect in the non-inertial reference frame of the Earth.