How do we know if the world is spinning or stationary? Do current images from space or the material in text books prove the Earth is spinning? Only if you believe the source to be valid. If, however, you are a natural scientist you would want to verify the veracity of the statements by repeating the experiments.
Using these two examples, let’s look at what is experienced when a person walks upon the earth. If the earth is spinning it is comparable to the conveyor belt example except that the earth’s axis acts as the central wheel that “belt” of the earth’s surface or ground moves around. It cannot be the train example since the floor of the train is not in motion. We can see that additional energy is provided by the moving ground whereas no additional energy is provided to the person who is beside the belt. We could then create an experiment where a person would leap against the direction of the belt (both on the belt and off). We could place an object 5 feet from the person both on and off the belt and ask them to leap towards the object. Since the additional energy of the belt is continually compelling the object forward, we would theorize that the total distance between the person and the object would be less than then person leaping beside the moving belt.
Why is leaping important in this experiment? If the person simply walks on the belt, the forward momentum will be continually added to the individual since there is always contact with the belt. By disengaging with the belt in a direction against the motion, we are subtracting (for a brief moment) the forward momentum of the belt and allowing the belt to move underneath. It would be possible to land nearer or even surpass the object whereas the person leaping beside the belt would gain no advantage like that. The question is how quickly does the forward momentum of the belt dissipate once the person leaps? If the person can leap (towards the object like a long jump) with an acceleration of 1 m/s/s and can stay airborne for 2 seconds then a total distance of 2m can be achieved (with a final velocity of 2m/s). Since the belt is moving at 1 m/s then in the first second the momentum has been overcome and the object has moved 1m closer. In the 2nd second the object moves 2m closer if we add the motion of the belt and the acceleration of the person. The total distance covered would be 3 meters. In the case of the person beside the belt, they would only be able to cover 2m if they leaped with the same acceleration. (you can work out the acceleration equation if you want)
We could increase the acceleration and distance by using something like a canon. If we use the same arc and acceleration the ball should land at a greater distance from the canon if on a moving belt than if stationary. If we assume that the acceleration of the canon is 10/m/s/s, the tennis ball can reach 80 m/s velocity and has a total airtime of 10 seconds, we can calculate the total distance travelled (640m). If the velocity of the belt is 1 m/s then within 1 second the momentum of the belt has been overcome and we can add an additional 9 seconds of belt movement to the distance for a total of 649m. If we then turn around and fire the canon in the opposite direction then the distance travelled by the canon is subtracted from the total distance of the ball (1m/s x 10 seconds = 10m). This would mean that the total distance between the canon and the ball would be 630m.
If we take the above example and apply it to a spinning earth then a similar result must take place. Taking the spin as the same as the conveyor belt one need only launch an object (a tennis ball thrower would suffice) to the west and then to the east. If the objects land at similar distances from the thrower then we are not spinning. However, if they land at different distances then we must be spinning.