Why do we usually talk about Newton's THREE laws?

[EL]

...when it is really only ONE law, one definition of "force" and one special case of that definition?

At least in all books I have read Newton's laws are numbered 1-3.
Anyone who knows why Newton called them all for "laws", and why we still stick to that?

[russ_watters]

I can see how 3 is a general statement of 2, but 1 is inertia and neither 2 or 3 say anything about it.

[chroot]

Well, F = ma says that in the absence of force, there is no change in velocity -- which is Newton's first.

- Warren

[hboregio]

That's exactly the question my Phyics teacher asked us and did not give the answer since he said it was for our final oral exam.... :s

[HallsofIvy]

Yeah! Ain't it awful when your professor actually expects you to THINK?M

[russ_watters]

Well, F = ma says that in the absence of force, there is no change in velocity -- which is Newton's first.

- Warren I thought about that, but since at the time of Newton that wasn't so self-evident, I think it still needed to be stated: If Newton's 2nd talks about acceleration due to a force, what about acceleration by other causes?

[Chronos]

Strangely disturbing.

[Zorodius]

How does the third law necessarily follow from the second?

[EL]

F=ma is a DEFINITION of "force".
The physics is in the law about an equally strong reaction force.

[no idea]

The three law is very useful and affect a lot of things

[pmb_phy]

Because they are all required -

Newton's First Law - A body at rest stays at rest and a body in motion remains in motion unless acted upon by a force

Newton's Second Law - The force on a particle equals the time rate of change of momentum, i.e. F = dp/dt. This gives Newton's first law when the force is zero, i.e. F = 0 -> dp/dt = 0 -> p = constant -> v = constant.

Newton's Third Law - Whenever there is an action there is an equal and opposite reaction, i.e. F12 = -F21.

The third law cannot be deduced from the first or second law. In fact it is not always true.

Pete

[B_orionis]

here's my professor's point of view:
the first law determines the reference frame in which the second law is correct(the inertial frame). The second law describes the way a dimentionless body moves in an inertial frame but it cannot be considerd as a definition of force. The third law "expands" the second one from particles to bodies.

[pmb_phy]

here's my professor's point of view:
the first law determines the reference frame in which the second law is correct(the inertial frame). The second law describes the way a dimentionless body moves in an inertial frame but it cannot be considerd as a definition of force. The third law "expands" the second one from particles to bodies.
There is a well known problem between the first and second law. That is that to define an inertial frame you have to define what "free-particle" or "absence of force" means. But to define force you have to define inertial frame.

In the words of Sir Arthur Stanley Eddington Every particle continues in its state of rest or uniform motion in a straight line except insofar that it doesn't..

Pete

[Galileo]

Newton's Third Law - Whenever there is an action there is an equal and opposite reaction, i.e. F12 = -F21.

The third law cannot be deduced from the first or second law. In fact it is not always true.


Are you saying the third law is not true? I'd like to see an example.

[EL]

pmb phy:
My point is that the first two should be seen as definitions and not laws.
So why are they still called "laws"?

Galileo:
The third law holds for central forces (e.g. gravity, electric).
The magnetic force (which is velocity dependent) is an example that doesn't obey the third law.

[Galileo]

The third law holds for central forces (e.g. gravity, electric).
The magnetic force (which is velocity dependent) is an example that doesn't obey the third law.

That depends on how you look at it.
If the third law doesn't hold, then conservation of momentum doesn't hold either it that case. The total momentum is not just the momentum of the particles that carry the charge, it is also in the fields. If there are no external forces acting on the system, then:
\frac{d \vec P}{dt}=0
where \vec P is the total (mechanical plus electromagnetic) momentum.
Or, in the case of two charged particles:
\frac{d \vec P_1}{dt}=-\frac{d \vec P_2}{dt}
which is Newton's third law.