Coriolis effect and water faucets?

The water faucet is obviously too small to see the coriolis effect. It can be an inspiration for a thought problem. Stipulate that while you are standing on the spinning earth, and you are extremely tall, except for at the poles, that your head is spinning faster than your feet, otherwise you would fall over. If you drop something from above your head, that thing since it is going faster than your feet, it will not drop at directly at your feet but off to the side. This is most true for something at the equator, and gradually less so as you move toward the poles. In the northern hemisphere, something dropped will seem to shift to more the further south it is. If you drop two things with a stick between them, one north of the other, the stick will appear to twist slightly as it drops since the southern one will move more than the northern. It will tend to twist the opposite direction on rising.