Look at the image: in the first picture the ball is moving over a rectilinear line on a stationary platform. The ball doesn’t resent of any lateral acceleration. When the platform starts rotating, the ball starts bending its trajectory and the result will prove to be a non rectilinear movement. This side acceleration is kown as Coriolis acceleration. It is an outstanding phenomenon that can be useful to prove that the Earth is not moving.
For example, let’s consider the ball as starting its linear movement exactly at the center of the circular platform. The platform rotates, let’s say, at the speed of 0.1 turn per second that means 6rpm i.e.0.628rad/sec.
The ball is initially on the center of the platform, so it cannot be dragged anywhere due to the peripheral speed of the platform because at the center it is actually zero and increases moving toward the periphery proportionally to the radius , according to the relation: Vp=ω*r where Vp is the peripheral speed, ω is the pulsation and r is the radius of the platform; r can vary from zero at the center to R that is the outer radius.
Thus when the ball starts its rectilinear movement from the center to the periphery of the platform it resents of this speed that constantly increases because of the radius increasing. The ball should start to have a lateral acceleration in the sense of rotation if it would maintain its rectilinear movement, but it can’t. Thus it starts to remain laterally backward due to inertia and the trajectory bends as it is shown in the picture.
Out of curiosity: the lateral acceleration that the ball should have to maintain in order to keep its linear trajectory could be expressed by this following formula: Ac=2*V*ω where Ac is the Coriolis acceleration, V is the speed of the ball and ω is the pulsation.
Lets apply now this idea to the globe and more specifically to airplanes that fly over the Earth.
An airplane moving on a pure east-west direction wouldn’t be affected by Coriolis effect because the speed of the globe on a fixed latitude doesn’t vary. But an airplane taking off from A would not arrive at point A'( as shown in the picture) unless its trajectory would be riadjusted by the aid of a suitable Coriolis acceleration ,then it would be able to arrive at point X.
When you make some research surfing the net, you will find that airplanes have some electronic system that can correct the trajectory in a suitable way. But is that actually true? Let’s investigate.
Consider, for example, a small airplane able to fly at a maximum speed of 500Km/h and taking off from the North Pole. The Earth wouldn’t drag it with its peripheral speed because the pole is on the axis, r=0, so Vp=0. Let suppose the airplane flies in an exclusively South direction and its speed has only one South component of 500Km/h. But something dangerous is happening under the airplane. As it continues to fly southwards the Earth below continues to accelerate due to its rotation in east-west direction as an effect of the increase of the radius, because r increases. When the airplane arrives to the equator, r=R i.e. 6371Km ,it should keep a perypheral speed of about 1700Km/h. Can the airplane correct its trajectory? No because even if it starts to follow the earth along the equator it can only reach 500Km/h. The fuel is finished, the airplane tries to land but it is destroyed in the same instant of its landing.
To the average reader this situation could seem too much theoretical. So let’s give him
an example taken from the everyday life. Imagine a man lying on his bed and ready to
get up. Imagine a treadmill (tapis roulant) moving under the bed at the level of his feet
at an amazing speed of 1000 km/ hour. Could the man be able to get up and
immediately start his activities? Absolutely not. He would be , with no doubt, hurtled
away from his bed and splattered somewhere against the wall.
This is a clear demonstration of the fact the earth is not moving around its axis. A
rotating earth would have to be moving fastest at the equator and slowest near the
north and south poles. But there is no difference in speed at any point on the earth’s
surface, whether north of, south of, or at the equator. Therefore the earth is not
rotating about its polar axis.
For a clearer explanation see this youtube video: Coriolis.