Every body perseveres in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces imposed upon it.
Examined superficially, this law appears to be only a special case of the second law, and hardly worth a separate statement. If a ~ F (Newton’s second law)2, it follows that in the absence of force there is no acceleration (Newton’s first law). Why then does the first law deserve the dignity of a separate statement as one of the fundamental laws of mechanics?
Several answers can be given to this question, some of them appreciated by Newton, others the result of later and deeper insights.
(1) Newton’s first law defines what kind of motion is “natural” or undisturbed motion, and thereby it delimits what kind of motion requires further explanation. According to Aristotle, the apparently circular motion of the Sun around the Earth does not require an explanation, because for heavenly bodies, circular motion is natural motion. On the other hand, Aristotle argued, the forward progress of an arrow through the air does require an explanation, in terms of some kind of motive power, because, as he saw it, the “natural” state of motion of the arrow is the state of rest or of vertical fall.3 Newton’s first law states instead that the constant horizontal component of the arrow’s velocity (in the absence of friction) is what is natural. This component, having no acceleration, requires no explanation in terms of force. On the other hand, the accelerated motion of the moon and planets, according to Newton, does require an “explanation,” that is, a description in terms of force. The first law makes clear that the planets, if undisturbed by outside influences, would move not in the circles envisioned by the ancients, but in straight-line trajectories off into space.
(2) There is a modern view of Newton’s first law that makes it truly independent of the second law, a view that was already implicit in Newton’s thinking about the laws of motion. A modern statement of the first law can be phrased this way: The center of mass of an isolated system free of external influences moves with constant velocity. This statement contains two improvements over Newton’s original statement of the law4 First, it replaces his word “body” by “center of mass.” Not all parts of a free body move with constant velocity; only its center of mass does so. Second, the new version of the law dispenses altogether with the concept of force. It is this aspect of the new statement that makes it significantly different from the original. As originally phrased by Newton, the first law suggested that one might first have to know what force is in order to know when none is present. Now it seems preferable to refer to “an isolated system free of external influences.” True isolation can never be achieved; but it can be approached. The new version of the law states that natural or undisturbed motion is achieved by removing a system to a very great distance from all possible outside influences. The significance of the law does not depend on any understanding of force. The concept of force then enters the theory of mechanics only through Newton’s second law.5
When Newton’s laws of motion are looked at in this way, there is a difference between an automobile moving down a straight road at constant velocity and a meteorite cruising at constant velocity in the depths of empty space. The automobile has no acceleration because the sum of all the forces acting on it happens to be zero. Its constant velocity merely illustrates a special case of Newton’s second law. The meteorite, on the other hand, directly illustrates Newton’s first law. That it should have constant velocity follows from its isolation, even if we knew nothing about force, or even if force had been inconsistently defined.
(3) In a way that Newton could not have foreseen, the separate formulation of the first law has been justified by history. We now know that Newton’s second law ceases to be valid in the submicroscopic world governed by quantum mechanics and in the high-speed world governed by relativity; and that in modern physics, the concept of force no longer plays a central role. The first law, on the other hand, at least when expressed in terms of momentum, remains valid, so far as we know, throughout all of nature. Its universally valid formulation is this: The total momentum of an isolated system free of all external influences is a constant. In the domains where Newtonian mechanics is valid, constant total momentum and constant velocity of the center of mass are equivalent. In the theory of relativity, however, the law of inertia can be expressed in only one way: in terms of momentum. Because the law of momentum conservation, the modern equivalent of Newton’s first law, is of such great importance, we can say that Newton’s first law, far from being a mere special case of the second law, is a pillar of modern physics. In the absence of external influences, a system retains constant momentum.
(4) Finally, Newton’s first law is significant in that it defines inertial frames of reference. It is literally true that the acceleration of an object depends on one’s point of view. In more technical language, it depends on the frame of reference of the observer. A motionless object seen by an accelerated observer seems to be accelerated. An accelerated object is, relative to an observer accompanying it, at rest. These facts mean that isolated systems are unaccelerated only for certain observers. The frames of reference of these observers are called inertial frames of reference. Only in inertial frames are Newton’s laws of motion valid.
1 The original is in Latin. This translation is by Andrew Motte, published by Daniel Adee in New York in 1846.
2 In the Principia, Newton defines mass as the “quantity of matter” but does not include it explicitly in his statement of the second law. Rather he states the second law simply as a proportionality.
3 Aristotle envisioned the air in front of the arrow dividing, then coalescing behind the arrow and pushing it forward.
4 Newton recognized the significance of the center of mass of a system of objects; he called it the center of gravity.
5 There are always subtleties! The center of mass of a system moves freely in the absence of outside influences only because internal forces (those among the parts of a system) add to zero—an implication of Newton’s third law. So the first and third laws are linked.