Synthesized answer
If a student only understood Law I, their understanding of the *cause* of changing motion would be incomplete because Law I states that a body perseveres in its state of rest or uniform motion unless acted upon by an impressed force [3]. This law identifies that forces cause changes in motion but does not quantify this relationship. It establishes the *necessity* of a force for change but not the *nature* or *extent* of that change in relation to the force [3].
Law II specifically addresses this gap by stating that "The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed" [3]. This law directly links the magnitude of the change in motion (alteration of motion) to the magnitude of the impressed force (motive force). It clarifies that a greater force will produce a greater change in motion, and a lesser force will produce a lesser change, with the changes being proportional [3]. It also specifies that the direction of this change in motion is aligned with the direction of the impressed force [3].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the…
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…
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…
e same time it will be found somewhere in the line CD. Therefore it will be found in the point D, where both lines meet. But it will move in a right line from A to D, by Law I. COROLLARY II. And hence is explained the composition of any one direct force AD, out of any two oblique forces AC and CD; and, on the contrary, the resolution of any one direct force AD into two oblique forces AC and CD: which composition and resolution are abundantly confirmed from mechanics. As if the unequal radii OM and ON drawn from the centre O of any wheel, should sustain the weights A and P by the cords MA and…
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.
- How does the second law's emphasis on "alteration of motion" and the direction of the "motive force" distinguish it from merely describing existing motion, and what does this imply about the nature of force itself?
- 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?