How important Coriolis force is

[tiny-tim]

Prompted by D H's post on inertial forces …

In General Relativity, the gravitational force is an inertial force, (or pseudo force, or fictitious force; they're synonyms). All inertial forces have one thing in common: They are proportional to the mass on which the force is acting. That gravitation is proportional to mass led Einstein to question whether gravitation is a real force, and that in turn led to the development of General Relativity.

… I've just read the fascinating wikipedia article on http://en.wikipedia.org/wiki/Fictitious_force" .

I hadn't previously understood how important Coriolis force is, even over small distances.

Coriolis force is (minus mass times) twice the cross-product of angular momentum of the frame, and the velocity of the object relative to the frame: -2mΩ x v.

(by comparison, centrifugal force depends on position rather than velocity, and is mΩ x (Ω x r))

So it depends on speed relative to the frame, and, for example, it is zero for a car moving uniformly in a circle and being observed by the driver of the car.

But that is the only circumstance in which the driver can ignore it.

In particular, it is twice the centrifugal force (and opposite to it) for stationary objects (like a house) being observed by the driver of that car:

The house has tangential velocity -mωr;
centrifugal force mω²r outward;
and Coriolis force 2mω²r inward;
net force: mω²r inward, forcing it to move in a circle round the driver! ​

Who'd 'a thought it! ​