As shown in the figure, the water surface in a rotating bucket will eventually become concave. The faster the rotating speed, the more concave the water surface is. The bucket in the left picture does not rotate very fast, so the water surface is not concave very much. The bucket in the right picture rotates very fast, so the water surface is concave very much. CONCLUSION: The faster the water rotates, the lower the pressure in the center of the bucket.
As shown in the figure, because the air flow on the right side of the ball is opposite to the rotation direction of the ball, the air flow on the right side of the ball rotates slowly; the air flow on the left side of the ball rotates in the same direction as the rotation direction of the ball, so the air flow on the left side of the ball rotates fast. According to the conclusion about the bucket, the pressure on the left side of the ball must be lower than that on the right side of the ball. So the ball will be exerted a right-to-left force F.
If the axis of rotation is parallel to the trajectory, there is no difference in rotation between the left and right sides of the ball. So it won't produce force F.