# Where did Newtons Second law come from?

1. Aug 18, 2013

### masscal

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.

2. Aug 18, 2013

### SteamKing

Staff Emeritus
Did you try 'Newton', 'Laws of gravitation' or 'Keplers laws of motion'?

3. Aug 18, 2013

### Philip Wood

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!

4. Aug 18, 2013

### masscal

You make it sound definitional or some how known a priori.

5. Aug 18, 2013

### Philip Wood

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: Aug 18, 2013
6. Aug 18, 2013

### Aero_UoP

I would suggest reading (not even study, just read) Newton's Philosophiae Naturalis Principia Mathematica...

7. Aug 18, 2013

### masscal

Doesn't it translate into near gibberish?

8. Aug 18, 2013

### Aero_UoP

come again...

9. Aug 18, 2013

### Staff: Mentor

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. Aug 18, 2013

### technician

repeated

11. Aug 18, 2013

### technician

probably.... the best way is to read modern text books 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. Aug 18, 2013

### Aero_UoP

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. Aug 18, 2013

### masscal

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. Aug 18, 2013

### D H

Staff Emeritus
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. Aug 18, 2013

### masscal

Reading from principia, he simply states the Three laws under "axiom, or laws of motion".

16. Aug 18, 2013

### D H

Staff Emeritus
17. Aug 18, 2013

### Filip Larsen

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. Aug 18, 2013

### masscal

Is there a digital copy?

19. Aug 18, 2013

### masscal

20. Aug 19, 2013

### Filip Larsen

I got my copy on Kindle for \$25, so that should be possible.