Newton’s Laws: What is Their Operational Meaning?

Newton’s mechanics is one of the most successful theories in the history of science; its success is based on three Newton’s laws. At first glance, the Newton’s laws that describe the relation between masses, forces, and accelerations are very clear and straightforward. However, the situation becomes more ambiguous if we take into account that the notions of mass and force are not operationally defined. In this paper, we describe the operational meaning of Newton’s laws. 1 It Is Important to Reformulate Newton’s Laws in Operational Terms: Formulation of the Problem Original formulation of Newton’s laws: reminder [1, 5]. The first Newton’s law – law of inertia – states that if no force is acting on a body, this body retains its speed and direction of motion. The second law states that the force F⃗ is equal to the product of mass m and acceleration a⃗: F⃗ = m · a⃗. The third law states that if a body A acts on a body B with a force F⃗ , then the body B acts on the body A with the force −F⃗ . Pedagogical problem: we need an operational reformulation. Of course, we have an intuitive notion of what is a mass and what is a force. However, for most people, these intuitive notions are somewhat vague, and to understand Newton’s laws, we need to be able to provide a precise numerical meaning of these terms. Without such operational meaning, Newton’s laws sounds very abstract: there exist some precise notions of mass and force for which the above three laws hold. This is probably how some students understand these laws. If all we have is such an abstract formulation, it is no wonder that some students have trouble applying these laws to real-life problems.