There has been much research on principles and fundamental concepts of mechanics. Problems concerning the law of inertia, the concepts of force, fictitious force, weight, mass and the distinction between inertial and gravitational mass are addressed in the first part of the present paper. It is argued in the second that the law of inertia is the source of these problems. Consequences drawn from the law explain the metaphysical concept of force, the problematic concept of fictitious force, the nominal definition of weight and the difficulty with defining mass operationally. The core of this connection between the law and these consequences lies in the fact that acceleration is a sufficient condition for force. The experimental basis of the law in the course of its history shows, however, that the law presupposes acceleration necessarily whereas acceleration does not presuppose the law. Therefore, there is no inconvenience in taking acceleration independently of the law. This is enough to bypass those problems. Taking into account how force is measured by force meters and how mass is basically determined, by comparison with the standard mass, a minimal meaning for both concepts of force and mass is established. All this converges with several solutions proposed in the course of history and increases the communicability of mechanics, as outlined in the final part of this paper.