Where did Newtons Second law come from?

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Discussion Overview

The discussion revolves around the origins and derivation of Newton's second law of motion, exploring its philosophical implications, historical context, and the relationship to earlier thinkers like Galileo. Participants express varying degrees of understanding and interpretation regarding how Newton formulated this law, including its dependence on experiential observations and its mathematical foundations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Historical
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about how Newton derived the second law, suggesting it is based on experiential observations.
  • Another participant argues that the justification of the law through experimental observations raises philosophical difficulties, particularly in measuring force independently of the law itself.
  • Some participants propose that Newton's second law could be seen as a definition of force, supported by practical experiences with physical systems like springs.
  • A participant mentions that Newton's first two laws were not original to him but were based on Galileo's work, emphasizing that Newton acknowledged this in his writings.
  • There is a suggestion to read Newton's "Philosophiæ Naturalis Principia Mathematica" for insights into his derivation, although concerns are raised about the accessibility of the text due to its historical context and mathematical style.
  • One participant notes that the second law can be derived from the first law, which is rooted in Galileo's observations about motion in different frames of reference.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the origins and derivation of Newton's second law. There are multiple competing views regarding its philosophical implications, its historical context, and the nature of its derivation.

Contextual Notes

Some participants highlight the challenges in measuring force and the implications of defining force in relation to Newton's laws. The discussion also touches on the historical contributions of Galileo and the complexities involved in interpreting Newton's original texts.

masscal
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I want to preface this question with the fact that I am a scum noob.

How did Newton come up with the second law of motion. As I understand it, it is only derived through experiential observations. I have tried many different Google searches but I can't find anything relevant.
 
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Did you try 'Newton', 'Laws of gravitation' or 'Keplers laws of motion'?
 
What better justification of a Law of Nature could you have than 'experiential observations'?

The philosophical difficulties with N2L are not, imo, that it's (only) justified by appeal to experiment, but that this can't be done satisfactorily because it's hard to come up with a way of measuring force that is independent of the law itself. Some physicists don't even think it's beyond dispute that two identical stretched springs in parallel will exert twice the force on a body that one such spring will do by itself.

I'll stop here. This question usually attracts lots of replies!
 
Philip Wood said:
The philosophical difficulties with N2L are not, imo, that it's (only) justified by appeal to experiment, but that this can't be done satisfactorily because it's hard to come up with a way of measuring force that is independent of the law itself. Some physicists don't even think it's beyond dispute that two identical stretched springs in parallel will exert twice the force on a body that one such spring will do by itself.

I'll stop here. This question usually attracts lots of replies!

You make it sound definitional or some how known a priori.
 
There are those who would argue that N2L is a definition of force. They might concede an a posteriori input: our experience with pulling things with stretched springs and so on suggests that such a definition would be useful. The usefulness is then confirmed by the appearance of force - replaceable (it is argued) by rate of change of momentum - in so many laws; Lorentz force on a charged particle, gravitational forces, and so on.
 
Last edited:
I would suggest reading (not even study, just read) Newton's Philosophiae Naturalis Principia Mathematica...
 
Aero_UoP said:
I would suggest reading (not even study, just read) Newton's Philosophiae Naturalis Principia Mathematica...

Doesn't it translate into near gibberish?
 
come again...
 
masscal said:
Doesn't it translate into near gibberish?

No, there are a number of decent translations out there. Reading it is serious work as Newton lacked many of the tools of modern mathematics and there was no generally accepted standard language for discussing physical concepts at the time, so I wouldn't recommend trying to learn mechanics from it.

But if you want an answer to a question of the form "How did Newton derive..." there's a lot to be said for looking at Newton's derivation.
 
  • #10
repeated
 
  • #11
masscal said:
Doesn't it translate into near gibberish?

probably... the best way is to read modern textbooks written by those who have studied Newton's writings. Such people are known as physicists...some of them are teachers !

PS... I have read the quoted book
 
  • #12
The exact question was "How did Newton come up with the second law of motion" and to that I answered!
He didn't ask "How can someone learn mechanics"...
 
  • #13
technician said:
probably... the best way is to read modern textbooks written by those who have studied Newton's writings. Such people are known as physicists...some of them are teachers !

PS... I have read the quoted book

They don't explain how he came up with the Laws of motions( at least my textbook doesn't), specifically the second law.
At first. I thought it was almost definitional like a unit of measurement but after some basic Google searches it sounds as if he used experimental data to derive it.
 
  • #14
Newton did not come up with his first two laws. They go back to Galileo, and Newton gave due credit to Galileo and others in his Principia. It was his third law that was uniquely his.
 
  • #15
D H said:
Newton did not come up with his first two laws. They go back to Galileo, and Newton gave due credit to Galileo and others in his Principia. It was his third law that was uniquely his.

Reading from principia, he simply states the Three laws under "axiom, or laws of motion".
 
  • #17
I can recommend "Worldviews: An Introduction to the History and Philosophy of Science" by DeWitt as a nice, readable introduction to the topic. It gave me a much better appreciation on how the foundation of modern science came about and how difficult it has been, and still is, for people to argue convincingly for what is meta-physically true.
 
  • #18
Filip Larsen said:
I can recommend "Worldviews: An Introduction to the History and Philosophy of Science" by DeWitt as a nice, readable introduction to the topic. It gave me a much better appreciation on how the foundation of modern science came about and how difficult it has been, and still is, for people to argue convincingly for what is meta-physically true.

Is there a digital copy?
 
  • #20
masscal said:
Is there a digital copy?

I got my copy on Kindle for $25, so that should be possible.
 
  • #21
masscal said:
I want to preface this question with the fact that I am a scum noob.

How did Newton come up with the second law of motion. As I understand it, it is only derived through experiential observations. I have tried many different Google searches but I can't find anything relevant.

Newton's second law is derived from his first law, which was really Galileo's. Galileo observed that the laws of physics are the same on a moving ship on a calm sea as on stationary land (1632 Dialogue). It was also assumed that all differently moving observers measured time the same. If those premises are true, then a unit of force applied for a unit of time to a unit of mass in the moving frame must result in the same change in motion for the same force applied for the same time to the same mass in the rest frame: fΔt = mΔv for all frames. If this were not the case, you could easily distinguish between moving and non-moving inertial frames, which contradicts the premise. From that it just requires a bit of mathematics to show that a = f/m.

AM
 

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