# I How Newton explained his law

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1. Jun 1, 2017

### Quantum Velocity

Hey guy!

I used google but it didn't help so can you guy pleas tell me how Mr.Newton explained his law please.

Thank!

Last edited by a moderator: Jun 1, 2017
2. Jun 1, 2017

3. Jun 1, 2017

### Quantum Velocity

No, thank you! What i want to know is why we have the law, the reason of the law action (the maximum explaination as we can in today world).

But by the way thank you for try to help me!

4. Jun 1, 2017

### vanhees71

It's a fundamental law within Newton's system of postulates. It cannot be derived from some other laws, you might consider more fundamental. As any fundamental law of physics it's entirely based on observation. Physical theories that are not based on a solid empirical basis are usually useless. There's not one example of a relevant physical theory in the entire history of physics which is not based on carefull observations of nature!

5. Jun 1, 2017

### Quantum Velocity

ooooooooooooooooooooooooooooooooooh!
Thank you, i got it!

6. Jun 1, 2017

### DrStupid

Newton's laws of motion can be (and most robably have been) almost completely derived from conservation of momentum.

7. Jun 1, 2017

### Quantum Velocity

But if the law is based on observation so can we explain it?

8. Jun 2, 2017

### vanhees71

What do you mean by explain? Of course, we can explain it. Obviously every high-school student who is introduced to Newtonian mechanics (I hope these are in fact all high-school students in the world) gets it explained in the first few lessons.

9. Jun 2, 2017

### DrStupid

I' not sure what you mean with "explain". If you just want wo know why we have Newton's laws of motion than the answer is: Because Newton published them. But I guess that is not not what you are actually asking for.

10. Jun 2, 2017

### Buffu

I know 3rd law but can you tell me how to derive 2nd law ?

11. Jun 2, 2017

### DrStupid

The 3rd is meaningless without the 2nd. You get both at once or none of them. For example: The 3rd law

$F_2 = k - F_1$

would result in the 2nd law

$F = \dot p + {\textstyle{1 \over 2}}k$

and vice versa. You can't derive them indepent from each other.

12. Jun 2, 2017

### Buffu

Why ? second says $F = ma$ and 3rd is about action and reaction. Third law is not concerned if force can be written in terms of other quantities or not.

What is $k$, $F_1$ and $F_2$ ?

13. Jun 2, 2017

### DrStupid

The second says that force is proportional to the change of momentum.
The third says that forces act pairwise and that these pairs cancel each other out.

How do you know what the third means without knowing the second?

What do you mean with "written in terms of other quantities"?

F1 is the force excerted from a body 1 to a body 2, F2 the the force exerted from body 2 to body 1 and k is a universal constant with the dimension of a force.

14. Jun 3, 2017

### vanhees71

Perhaps the more modern view on physical theories is more convincing for you than Newton's quasi-axiomatic approach? As I said before, Newton's postulates are deduced from observation. Famously Newton said "hypotheses non fingo" (I don't invent hypotheses).

The modern point of view is to use the action principle to formulate fundamental dynamical laws and employ symmetry principles to constrain the possible action functional. For Newtonian mechanics the symmetry is Galileo symmetry of Newtonian spacetime. It postulates that space and time are homogeneous (i.e., no point in space is preferred compared to any other and no point in time is preferred compared to any other), space is Eulidean and thus also isotropic. Finally there exists an inertial frame, and it's not possible to distinguish any inertial frame from any other, i.e., the physics is also invariant under Lorentz boosts (i.e., changing from one inertial frame to another one moving with constant velocity relative to the former). This implies 10 conservation laws according to Noether's theorems, and the generators are energy (Hamiltonian) (time translation invariance), momentum (space translation invariance), angular momentum (isotropy of space), and the center-of-mass velocity (boosts). In this approach the somewhat problematic idea of "force" is a derived concept, and the form of the laws is founded on symmetry principles.

This idea is crucial for an understanding of modern theories, particularly special and general relativity which introduce new space-time models and quantum theory, where the symmetry principles define the operator algebras of observables.

15. Jun 6, 2017

### Quantum Velocity

But im only in 8th grade so can you explain it to me vanhees71

16. Jun 6, 2017

### Staff: Mentor

You may have to accept that you're just not ready for a more complicated explanation at the moment. Give it a few years, develop your skills a bit more, and then it may make more sense.

17. Jun 7, 2017

### Quantum Velocity

Ok thanks for help!

18. Jun 7, 2017

### Ibix

What @vanhees71 said is stuff I didn't come across until my second year in university. It requires a fairly advanced application of calculus, so you're going to need to learn a lot of maths before you can follow it with any rigour.

In short, there are several different starting points you can use to build on and end up with the same equations of motion. Newton started with his three Laws. Lagrange and others derived the same thing from rather more abstract principles. Lagrange's approach is more flexible in many ways, but much more mathematically complex.

But there's no getting away from the fact that there are some basic assumptions (Laws, or postulates) that cannot be proved. The only justification we offer for them is that the results match reality as precisely as we can test. (Or not, in the case of Newtonian mechanics, which is why Einstein developed relativity).

Last edited: Jun 7, 2017