Synthesized answer
The passages show that the second law defines force as the cause of *change* in motion, not motion itself. Law II states that "the alteration of motion is ever proportional to the motive force impressed" [2], and Law I establishes that a body continues in its state of motion unless compelled to change by an impressed force [2]. This emphasis on "alteration" distinguishes force from merely describing existing motion, because force is what produces a deviation from uniform rectilinear motion, as seen in Proposition II where a body moving in a curve is "turned aside from its rectilinear course by the action of some force" [3].
The direction of the motive force is also specified: the alteration "is made in the direction of the right line in which that force is impressed" [2]. This implies that force is inherently directional and vector-like, as the resulting motion is compounded from the original motion and the impressed force, whether they "directly conspire with or are directly contrary to each other; or obliquely joined" [1]. Thus, force is not a property of motion itself but an external agent that changes motion in a specific direction.
The passages do not explicitly discuss the…
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
ortional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are…
← Definitions The Mathematical Principles of Natural Philosophy (1846) by Isaac Newton , translated by Andrew Motte Axioms, or Laws of Motion Section I → 596269 The Mathematical Principles of Natural Philosophy (1846) — Axioms, or Laws of Motion Andrew Motte Isaac Newton AXIOMS, OR LAWS OF MOTION. LAW I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force…
hich are placed in those planes, are not at rest, but move uniformly forward in right lines. PROPOSITION II. THEOREM II. Every body that moves in any curve line described in a plane, and by a radius, drawn to a point either immovable, or moving forward with an uniform rectilinear motion, describes about that point areas proportional to the times, is urged by a centripetal force directed to that point. Case . 1. For every body that moves in a curve line, is (by Law 1) turned aside from its rectilinear course by the action of some force that impels it. And that force by which the body is turned…
crew may be deduced from a like resolution of forces; it being no other than a wedge impelled with the force of a lever. Therefore the use of this Corollary spreads far and wide, and by that diffusive extent the truth thereof is farther confirmed. For on what has been said depends the whole doctrine of mechanics variously demonstrated by different authors. For from hence are easily deduced the forces of machines, which are compounded of wheels, pullies, levers, cords, and weights, ascending directly or obliquely, and other mechanical powers; as also the force of the tendons to move the bones…
← Section I The Mathematical Principles of Natural Philosophy (1846) by Isaac Newton , translated by Andrew Motte Book I, Section II. Section III → 597082 The Mathematical Principles of Natural Philosophy (1846) — Book I, Section II. Andrew Motte Isaac Newton SECTION II. Of the Invention of Centripetal Forces. PROPOSITION I. THEOREM I. The areas, which revolving bodies describe by radii drawn to an immovable centre of force do lie in the same immovable planes, and are proportional to the times in which they are described. For suppose the time to be divided into equal parts, and in the first…
More questions about this book
- Explain Newton's First Law of Motion, using only the provided examples, in a way that clarifies what "perseveres in its state" truly means for both rest and uniform motion.
- If a student only understood Law I, how might their understanding of the *cause* of changing motion be incomplete, and how does Law II specifically address this gap?
- Beyond a simple definition, what characteristics of "forces" can be inferred solely from their described effects in Laws I and II, and what implications does this have for observing physical phenomena?
- Given the initial context of Euclid and the title "Axioms," what significance might Newton have intended by presenting these fundamental principles as "Axioms, or Laws of Motion" rather than hypotheses or observations?