Newton's Laws
In Philosophiae Naturalis Principia Mathematica, the natural philosopher Isaac Newton formulated three fundamental principles of mechanics, now known as Newton's Laws of Motion.
These axioms form the foundation of classical mechanics and can be summarized as follows:
Newton's Laws
- A body not acted upon by external forces remains in uniform motion in a straight line or at rest. In other words, if no net force acts on a body, its velocity remains constant:$${\vec{F} = 0\Rightarrow\left\{\begin{array}{l}\vec{v} = 0\\ \vec{v} = \text{const}\end{array}\right.}$$
- The net force $\vec{F}$ acting on a body is proportional to its acceleration $\vec{a}$, with the mass mm as the proportionality constant: $${\vec{F} = m\vec{a}}$$
- If a body 1 exerts a force $F_{1\rightarrow 2}$ on a body 2, then the opposing force $\vec{F}_{2\rightarrow 1}$ of equal magnitude but opposite direction acts on body 1. Therefore, the following applies: $${\vec{F}_{1\rightarrow 2} = -\vec{F}_{2\rightarrow 1}}$$ This relationship is therefore also referred to as the action-reaction principle.
These laws are termed axioms because they are not derived from more fundamental principles - they are based on observation and experimentation.
Interpretation
Regarding Newton's first axiom, it should be noted that this initially seems to contradict one's own intuition, since almost all moving everyday objects slow down over time unless they are constantly driven. This can, however, be explained by the presence of friction, which acts as an additional force to slow down all bodies.
The quantity force can be defined via Newton's second law. If one replaces acceleration $a$ with the acceleration due to gravity $g$, it becomes clear that $g$ must have the unit $\mathrm{m/s^2}$ as well as the unit $\mathrm{N/kg}$ to be satisfied. $g$ is therefore also referred to as the location factor, as it serves as a conversion factor between weight (gravity) and mass. However, the term weight has become colloquially accepted as a synonym for mass.
Experiment
To demonstrate Newton's second law, a heavy ball is suspended from a string. Another string is attached to the bottom of the ball. If you pull slowly, the upper string breaks and the ball falls to the bottom. If you pull quickly on the lower string, it breaks and the ball doesn't move because the force couldn't be transferred to the ball due to its inertia.
Experiment
Newton's third law can be illustrated using two skateboards. A person stands on each skateboard, each holding one end of a rope. When one person pulls on the rope, both people still move toward each other.