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I believe that more lies are told about the Coriolis force than about any other force on Earth! This is true partly because the Coriolis force is so difficult to detect, and it certainly can't be "felt" by the human body. Some of the untruths deal with what the Coriolis force actually is, some deal with demonstrations of how the Coriolis force works, some deal with how the Coriolis force acts on an air parcel, and some deal with what the Coriolis force does to things like a draining bathtub.
What the Coriolis force actually is
I suppose I'm guilty of lies just like everyone else, because I've explained exactly half of the Coriolis force: the half due to the changing orientation of the coordinate system with respect to a velocity vector. There's another half too, which is exactly equal, and is due to alterations in the centrifugal force experienced by a object moving with respect to a rotating coordinate system.
Consider something moving east-west, along a latitude line. The object's motion about the Pole will be faster or slower (depending on which way it's going) than the motion of the Earth beneath it. Thus, it will feel a slightly different centrifugal force because of its velocity. Since what we call the "centrifugal force" is the acceleration associated with the rotation of the Earth itself, the other part of the centrifugal force gets folded in with the Coriolis force.
Now consider the real motion of stationary objects on the surface of the Earth with respect to the Earth's Pole. An object near the Pole moves very slowly - it doesn't have to cover much distance to make a complete circle around the Pole in one day. By contrast, objects near the Equator travel quite rapidly to make it all the way around the Earth: the speed of the Earth's surface near the equator (relative to the Pole) is about 1000 miles per hour!
Now consider something moving north-south, away from the Pole. As it moves farther than the Pole, the surface of the Earth beneath it is traveling faster and faster. If no true forces act on the object, it will move slower and slower compared to the Earth beneath it, causing an apparent deflection in its direction of motion. The deflection is proportional to its velocity: the faster the object changes latitude, the sooner it experiences the differently-moving Earth.
In the northern hemisphere, both these effects (east-west motion + the centrifugal force, and north-south motion + the speed of the Earth) cause a deflection to the right that's exactly equal to the deflection caused by the change in orientation of the rotating coordinate system. For velocities other than north-south and east-west, the combination of the two effects is still always equal to the change in orientation effect. Consequently, the full Coriolis force is twice as large as the change in orientation effect would suggest.
I've actually shown this already. Notice that at the endpoint of the ball's path, the direction of motion of the ball has changed TWICE AS MUCH as the angle of the sun with respect to the runway and the observer.
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