sigma said:
Pervect:
But after what I understand the Coriolis force is a force acting on a body moving in a rotating reference frame. What I need to calculate is the balls' movment with respect to a rotating reference frame. The ball is rotating with the same angular velocity as Earth as long as it is held over the point. Once dropped it will try to maintain the same velocity and direction (a straight path) while gravity will try (and probably succeed) to pull the ball to the ground. Gravity is the only force acting on the ball. Or have I got the concept wrong?
Why are you skeptic about 2? Gravity is commonly threated as a force parallell to the y-axis in euclidean space. That is not a problem when throwing pebbles across the schoolyard but this model breaks down if you want to calculate sattelite or planet orbits (or if you want to impress my physics teacher

). I'm just not sure what reference frame to choose and what maths to apply.
There are two approaches you could take. The first approach is to do physics in a rotating coordinate system. This is the approach I was suggesting - but on second thought, it may not be the best approach. In this approach, you need to include "pseudo-forces", such as the centrifugal force, and the coriolis force. These are sometimes called general forces. If you choose to do the problem in a non-inertial coordiante system, you must use pseudo forces. If you choose to do the problem in a truly inertial coordinate system, you must _not_ use pseudoforces. Sometimes beginning students are cautioned strongly not to use non-inertial coordinate systems, if this is the case you should follow your instructors guidelines.
If you do use the non-inertial rotating coordinate system, you can write down equations for the drop of the ball which say that the total acceleration on the ball is given by the force of gravity (downwards), the centrifugal force due to the rotation of the Earth (upwards), and the coriolis force (sidewards, proportional to the velocity of the ball). You would have to integrate the coriolis force over time to get the total displacement.
But it may be simpler to do the problem in an inertial coordinate system, as Tom Matheson suggested. This avoids the concept of pseudo-forces at all, which may be a bit confusing. When you do the problem in an inertial coordinate system, you are correct in saying that the only force on the ball is gravity. In this approach, you stick an x-y coordinate frame through the center of the earth. You then say that the Earth's surface follows the equations of motion x = r*cos(w*t), y=r*sin(w*t). Note that the Earth's surface is accelerating due to it's rotation. You then say that the ball moves with an initial velocity of vy=(r+h)*w. The total force downwards on the ball will be G*m*M/r^2. Note that this force will be greater than the weight of the ball at rest on the equator, due to the very small centripetal acceleration of the Earth's surface. In theory, the dirction of the gravitatoinal force will always be towards the center of the earth, which is changing, which is what I think you were worried about. But the variation of the direction of the gravitational force in this problem is going to be very small, so you can safely approximate it as a constant acceleration in the 'x' direction, unless you are really ambitious. If you are really ambitious, you can solve the Kepler problem for the orbit of the body moving with the initial velocity specified to describe the motion of the body.