More and more my teacher has talked about how results for mechanical problems are the same no matter what our coordinate system is (though it may be easier to calculate them in some coordinate frames). I must however admit, that I have never really had a clear explanation of what it means to do a problem in different coordinates. Suppose we have a point mass sliding down a frictionless slope and want to find its acceleration. We project the force of gravity onto the direction parallel to the slope and find the acceleration of it. Is this procedure of splitting your force vector into vectors in different directions, what is meant by shifting the coordinate frame? Because if so, how would you ever solve a problem in another frame than the one with axis parallel to the slope and perpendicular to it?