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It seems clear that Newton's first law is a special case of his second. Although perhaps people might argue that it emphasizes the centrality of inertial frames.

But is the third law also just a special case of the second? Could a physical system exist which obeyed the first two laws but not the third? Or does the third again simply emphasize an aspect of the second that is useful didactically?

Responding to a comment about why the third is a subset of the second, take an example of an object sitting on a table. The object has gravity pulling down but it is not accelerating so the net force must be 0 (from N2). Similar logic can be applied to other situations (I think). At least, that's what this question is trying to clarify.

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Historically, people thought that a projectile needed a continuing force to keep it moving through the air. Newton's first law cleared this misconception up by stating that due to an object's inertia, that object will preserve its state of motion until an outside force acts on it.

Newton's second law provides an equation that can be used to calculate how much force is required to change an object's state of motion by a given amount.

Historically and still today, there is a huge misconception that when a big object collides with a small object, the big object imparts a big force on the small object, and the small object imparts a small force on the big object. Such a situation seems intuitively obvious, but it is wrong. Newton clarified this situation by stating that the forces between objects are equal in magnitude and opposite in direction, even when field forces are involved (and in fact, all fundamental forces are field forces).

Newton's law 1 and law 3 are NOT restatements of the second law. Laws 1 and 3 necessarily need to be formally stated to eliminate the misconceptions that most people take to be intuitively obvious, but are wrong.

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  • $\begingroup$ I accept the usefulness for teaching purposes. But can you give me an example of a theoretical physical system in which N2 is obeyed but N3 is violated? $\endgroup$ – Dr Xorile May 14 at 17:13
  • $\begingroup$ @DrXorile: Not really. If you violate N3, then you're not conserving momentum, and then the whole thing just doesn't make physical sense. $\endgroup$ – Kevin May 14 at 17:21
  • $\begingroup$ @Kevin, it could be a hypothetical model or a computer model. But if what you say is generally true, then N3 is implied by N2. $\endgroup$ – Dr Xorile May 14 at 17:31
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    $\begingroup$ @DrXorile: No. N3 is implied by N2 and "The laws of physics are uniform in space." If you don't have the latter, you cannot infer N3. It's just that, if the laws of physics are not uniform in this manner, then the resulting physics will be quite bizarre indeed. $\endgroup$ – Kevin May 14 at 17:58
  • $\begingroup$ @DrXorile Magnetic forces between moving charged particles do not obey Newtons' third law. But magnetic forces are outside the scope of Newtonian mechanics, it takes relatitivistic electromagnetic theory and relativistic mechanics to understand them. $\endgroup$ – Ján Lalinský May 14 at 23:25

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