Are Newton's three laws of motion essentially correct

[InvariantBrian]

Newton's three laws are;

1. Inertia
2. f=ma
3. for every action there is an equal an opposite reaction.

It seems to me that the first and third law are still valid with the theory of relativity. And the second law f=ma is generally true in so far as it is correct to say that there exists an invariant universal relation between force mass and acceleration. Newton did not know that time, space and mass vary with respect to velocity. But I am inclined to say that Newton's ideas were incomplete rather than simply wrong. I am interested in what others may have to say about this.

Thanks

Brian.

 

[pervect]

To go from Newton's laws to the relativistic version, let P be the momentum

Newton

p=mv, F=dp/dt

Relativistic

p=mv/sqrt(1-(v/c)^2), F=dp/dt

 

[InvariantBrian]

oh that's interesting. So you can update Newton's second Law? and do you agree about the first law and the third?

 

[omin]

And the second law f=ma is generally true in so far as it is correct to say that there exists an invariant universal relation between force mass and acceleration. Newton did not know that time, space and mass vary with respect to velocity. But I am inclined to say that Newton's ideas were incomplete rather than simply wrong.

I see the general principle in the second law covering the basis of every theory possible. Its seems to tie any type of velocity with any type of acceleration. For example, "time, space and mass vary with respect to velocity", proves a constant is needed to test for acceleration rate. Otherwise, we would have no idea how much anything varies and would call it unquantifiable. But unquantibiable is limited only by the precision of what we can sense through our basic senses direct or through indirect instrumentation aided sensing. I'd say, Newton hit it on the head and no theory will every out do the second law, in terms of comparision, the basic principle of physics.

 

[HallsofIvy]

Newton's three laws are;

1. Inertia
2. f=ma
3. for every action there is an equal an opposite reaction.

It seems to me that the first and third law are still valid with the theory of relativity. And the second law f=ma is generally true in so far as it is correct to say that there exists an invariant universal relation between force mass and acceleration. Newton did not know that time, space and mass vary with respect to velocity. But I am inclined to say that Newton's ideas were incomplete rather than simply wrong. I am interested in what others may have to say about this.

Thanks

Brian.

The only thing I find peculiar about this is that it implies that someone MIGHT say that Newton was wrong! Newton was amazing correct for the situation he was talking about. Relativity just extends it to extreme speeds and extreme masses comparitively. In any case there is no such thing as a "perfect" theory. Even relativity is not 'complete' because we don't know everything. It will, eventually, be superceded by a more accurate theory- this is the nature of the scientific process. (Actually, so much has been added to or 'adjusted' on relativity, one could argue that it has already been superceded.

 

[Ba]

The change in velocity (acceleration) with which an object moves is directly proportional to the magnitude of the force applied to the object and inversely proportional to the mass of the object.

This actually is Newton's second law of motion and is phrased in a way that it actually fits in with relativity. At least it seems so to me.

 

[pervect]

oh that's interesting. So you can update Newton's second Law? and do you agree about the first law and the third?

Personally I think it's simpler to think of Newton's laws as saying that momentum is a conserved quantity, and that force is the rate of change of momentum. Relativistic dynamics is basically the same as Newtonian dynamics with a slightly different definition of momentum.

Therre are several ways besides Newton's laws to get classical mechanics, among the most interesting is the principle of least action, often known as Hamilton's principle.

an online java applet which illustrates this approach is at:

http://www.eftaylor.com/software/ActionApplets/LeastAction.html

a good encylopedia article (but it gets technical fast) is:

http://en.wikipedia.org/wiki/Euler-Lagrange

 

[mijoon]

I don't know why anyone would call them incorrect.They are a specific case of the more general principals of GR. It is likely, that we will one day view GR also as a specific case of some even more general theory.
That doesn't make Newton incorrect, nor would it make Einstein wrong.

 

[InvariantBrian]

But isn't there some type of electromagnetic phenomena that violates the third law?

 

[Antonio Lao]

But isn't there some type of electromagnetic phenomena that violates the third law?

The 3rd law is based on central forces. The magnetic force is not a central force.

 

[robphy]

But isn't there some type of electromagnetic phenomena that violates the third law?

These problems with the Third Law for electromagnetic phenomena arise when the interaction takes place over a distance ("action at a distance").

Note that the Third Law is an instantaneous statement
\vec F_\text{on A due to B} = -\vec F_\text{on B due to A}\quad \text{"now"}.
Since electromagnetism is really a relativistic theory (where distant simultaneity [what "now" is] is observer-dependent), the introduction of the electromagnetic field saves the third law [in the sense that the field carries momentum] since the interaction is now local (as they are for contact forces).

 

[Antonio Lao]

The 3rd law in the form

F_{12}+F_{21}=0

is really time independent. It is true in the past, at present, and in the future. But in the form

m_1 a_{12}+m_2a_{21}=0

the accelerations come into being the instant the masses come into existence. But if the masses are equal then the accelerations are equal in magnitudes but opposite in directions. The result is no accelerations, the masses are either at rest or move at constant speed as a group of 2-body system. Zero accelerations imply constant velocity. And this constant velocity can be the speed of light in vacuum.

 

[Antonio Lao]

for attractive force, the accelerations exist up to half the distance between the two point-particles. But the mass ratio equalling to the negative ratio of two vectors of acceleration does not make any sense.

\frac{m_1}{m_2}= - \frac{\vec{a}_{21}}{\vec{a}_{12}}

I could be mistaken, but in order to define mass ratio, another conservation law must be invoked. This is the conservation of angular momentum.

 

[pmb_phy]

Newton's three laws are;

1. Inertia
2. f=ma
3. for every action there is an equal an opposite reaction.

It seems to me that the first and third law are still valid with the theory of relativity. And the second law f=ma is generally true in so far as it is correct to say that there exists an invariant universal relation between force mass and acceleration. Newton did not know that time, space and mass vary with respect to velocity. But I am inclined to say that Newton's ideas were incomplete rather than simply wrong. I am interested in what others may have to say about this.

Thanks

Brian.

In going to special relativity;

First Law - Newton's first law remains valid.

Second Law - The second law remains valid as well. However you wrote it down incorrectly. Newton's second law is not F = ma. Its F = dp/dt. Only when m = constant does F = ma. Even Newton didn't hold that F = ma. Newton held that force is proportional to changes in momentum. In SR Inertia is properly though of as a bodies resistance to changes in momentum.

The definition of momentum remains valid as well. I.e. momentum is still given by p = mv. For tardyons (particles for which v < c) m = m(v) = m₀/(1 - v²/c²)^1/2 where m₀ = m(0) (m₀ is what pervect labels "m"). m₀ is called proper mass or sometimes rest mass (I dislike the term "rest mass" myself). For a derivation please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm

If anyone notices any errors on this page please let me know. Thanks.

Third Law - Newton's Third Law is not always valid even in non-relativistic physics. It sometimes fails when there are charges involved. But in SR it always holds for contact forces.

Note - Everything above applies to particles. If the object in question is not a particle then p = m₀v/(1 - v²/c²)^1/2 is not always valid. For example, a rod which is moving in the direction parallel to its length. If the rod is loosing mass uniformly in its rest frame (e.g. by emitting radiation uniformly along its length) then p = m₀v/(1 - v²/c²)^1/2 does not hold. The relationship is more complicated. See the bottom of this page

http://www.geocities.com/physics_world/sr/invariant_mass.htm

If the mass of the rod is constant but is under stress then the momentum not given by p = m₀v/(1 - v²/c²)^1/2 either. Stress adds to inertial mass but it only does so when the body is moving. For an example which will shed light on this see

http://www.geocities.com/physics_world/sr/rd_paradox.htm

I'm working on another example but I've put it aside for the time being. I'll get back to it next year.

Pete

 

[InvariantBrian]

But can Newton's third law be interpreted in such a way as to make it correct?

I found the following statement on the web...

'It is often contended that Newton's third law is
incorrect when electromagnetic forces are included: if
a body A exerts a force on body B, then body B will in
general exert a different force on body A (the force
considered is the Lorentz force, generated by electric
and magnetic fields). Modern theory predicts that the
electromagnetic field generated by such interactions
itself transports momentum via electromagnetic
radiation. Newton's third law becomes correct if the
momentum of the field is included in the calculations'

could you please comment on this statement?

thank you.

 

[InvariantBrian]

The 3rd law in the form

F_{12}+F_{21}=0

is really time independent. It is true in the past, at present, and in the future. But in the form

m_1 a_{12}+m_2a_{21}=0

the accelerations come into being the instant the masses come into existence. But if the masses are equal then the accelerations are equal in magnitudes but opposite in directions. The result is no accelerations, the masses are either at rest or move at constant speed as a group of 2-body system. Zero accelerations imply constant velocity. And this constant velocity can be the speed of light in vacuum.

I am not a science major. Is the above equation an interpretation of Newton's third law that is valid today?

thank you.

 

[trendy]

first law

I am sorry to interrupt this nice discussion but I need an answer to a question that I couldn't find on the web.

Why does Newton's first law hold? I mean is there an explanation why does an object in motion tend to stay in motion? Is this still a principle derived from observation or we can explain it?

Thanks.

 

[Antonio Lao]

I am not a science major. Is the above equation an interpretation of Newton's third law that is valid today?

Newton's laws of motion is based on the concept of mass. The forces are all central forces. When masses are in motion, these define a concept of momentum. In my own opinion, the conservation of momentum, which is implied in the 3rd law, should be the 1st law, and the 1st law move to being the 3rd law. The 1st did mention a force but the 3rd law of action and reaction directly or explicitly defined the force. This force exists only if there are at least two bodies involve in the interaction. So, we can say all interactions are 2-body but by the superposition principle, all these 2-body interactions can be added together. Newton's laws as summarized in the law of conservation of linear momentum is as valid today as it was yesterday.

The theory of electromagnetism as formulated by Maxwell is based on the concept of electric charge. The Lorentz force, though still conservative (conservation of electric charge), has a non-central magnetic force. It can also be noted that mass does not appear in the Lorentz force equation.

But in order to determine the constants of these theories, both the force of gravity and force of electromagnetism must be used in the experimental laboratories. What we ended up is the charge to mass ratio and then independently find the unit of charge (quantum of charge). But as of now, we still do not have a value for the quantum of mass. From my own research, I am hypothesizing that the Planck mass is the quantum of mass and it has a positive and a negtive value. Yet we have to explain why the mass of the electron is only 1/2 MeV.

 

[InvariantBrian]

But if Newton's third law is stated in these two equations, does it adequately account for the force interactions in electric charges?

m_1 a_{12}+m_2a_{21}=0

F_{12}+F_{21}=0

 

[Antonio Lao]

InvariantBrian,

It does not. Newton's laws of force are for the inertial force (2nd law) and the law of universal gravitation. Both of these forces depended on the concept of mass only.

The concept of electric charge as formulated by Maxwell was invented about 200 years after the death of Newton. The force that depended on the concept of electric charge is called the Lorentz force, the sum of electric force and magnetic force.

The force that depended on the weak charge is called weak nuclear force.

The force that depended on the color charge is called strong nuclear force.

Although all charged particles also have mass, the effect of these force-from-mass are negligible by comparison to the other forces. The strength of each force is the coupling constant determined by experiments for each force.

 

[InvariantBrian]

Thank you for answering my question. I appreciate it. but I am confused...I found this quote on the web...

"It is often contended that Newton's third law is
incorrect when electromagnetic forces are included: if
a body A exerts a force on body B, then body B will in
general exert a different force on body A (the force
considered is the Lorentz force, generated by electric
and magnetic fields). Modern theory predicts that the
electromagnetic field generated by such interactions
itself transports momentum via electromagnetic
radiation. Newton's third law becomes correct if the
momentum of the field is included in the
calculations."

Do you think the above statement is correct?

thanks again

 

[Antonio Lao]

Do you think the above statement is correct?

It is correct if and only if both body A and body B are charged particles. When both are at rest (static), there is no magnetic field. Magnetic field is generated for any of the moving charged particles. But the electrostatic field will also cause the charged particles to move. The electrostatic force is the Coulomb's force which is similar to the gravitational force, but the gravitational force is equivalent to the inertial force of Newton's 3rd law of motion. So, the inertial force and the Coulomb's force are essentially equivalent. They are central forces. But the magnetic force is not a central force. It is given by

F_B=q \vec{v} \times \vec{B}

where q is the electric charge, v is the velocity of the charge, and B is the magnetic field generated by the moving charge. Because of the vector product, the resultant magnetic force is not a central force. The magnetic force does not act along the line joining the two moving charged particles. It acts perpendicular to the plane containing the velocity vector and magnetic field vector. The Lorentz force is given by

F_L = q \vec{E} + q \vec{v} \times \vec{B}

where E is the electric field. This Lorentz force is equivalent to the inertial force if and only if the magnetic field is zero. But for charged particles, the magnetic field will never be exactly zero. Therefore, the inertial force can never be fully equivalent to the Lorentz force. But they can still be equivalent at time equal zero.

 

[Antonio Lao]

Modern theory predicts that the
electromagnetic field generated by such interactions
itself transports momentum via electromagnetic
radiation.

The momentum of the EM field is given by

p=\frac{E}{c}=\frac{h\nu}{c}

where \nu is the frequency of the EM waves. h is Planck's constant. c is the speed of light in vacuum.

This expression established the quantum theory of radiation leading to the existence of photons. It is this idea of the photoelectric effect that gave Einstein the Nobel Prize in 1921.

 

[InvariantBrian]

well, let me ask a question. If Newton's third law were really violated, would it not follow that the conservation of momentum would also be vilotate?

 

[Antonio Lao]

So far, the conservation of momentum has not been violated. Although, in the quantum domain, the conservation of parity has been violated. The conservation of CP has also been violated. But, ultimately, scientists believe that the conservation of CPT will not be violated.

 

[InvariantBrian]

So far, the conservation of momentum has not been violated. Although, in the quantum domain, the conservation of parity has been violated. The conservation of CP has also been violated. But, ultimately, scientists believe that the conservation of CPT will not be violated.

But my argument is this...

If Newtons third law really be violated, it follows that the conservation of momentum could be violated.

But since the conservation of momentum cannot be violated, it follows that Newtons third law cannot be violated either

what do you think

 

[Antonio Lao]

InvariantBrian,

Let's just say that Newton's 3rd law will definitely be violated if there is only one object in the universe. One you no me or one me no you. There will be no action or reaction. You'll be talking to yourself or I'll be talking to myself.

Maybe that is why, in holism, the whole is believed to be greater than the sum of its parts. It's th missing parts that need to be intelligible as well as sensible. So far, we human have failed in trying to understand these parts of existence but in science, and physics in particular, we called these parts the fields and the knowable parts as the particles. And from understanding the particles we hope to understand the fields in a quantum field theory (QFT).

There always, at the least, must be two objects in order for the law of conservation of linear momentum to hold. And the application can only be done to two objects at a time, it's not a 3-body law (but the "field" is supposed to be composed of infinite bodies) but a law only for 2-body interaction with respect to a given time interval or measure.

 

[InvariantBrian]

InvariantBrian,

Let's just say that Newton's 3rd law will definitely be violated if there is only one object in the universe. One you no me or one me no you. There will be no action or reaction. You'll be talking to yourself or I'll be talking to myself.

Maybe that is why, in holism, the whole is believed to be greater than the sum of its parts. It's th missing parts that need to be intelligible as well as sensible. So far, we human have failed in trying to understand these parts of existence but in science, and physics in particular, we called these parts the fields and the knowable parts as the particles. And from understanding the particles we hope to understand the fields in a quantum field theory (QFT).

There always, at the least, must be two objects in order for the law of conservation of linear momentum to hold. And the application can only be done to two objects at a time, it's not a 3-body law (but the "field" is supposed to be composed of infinite bodies) but a law only for 2-body interaction with respect to a given time interval or measure.

Actually, if there was only one object in the universe, Newton's third law would definitely not be violated because there would be no action/reaction at all.

THe law states that for every action there is an opposite equal reaction.

If there are no action/reactions, nothing has been violated.

it would not even get a chance to be violated.

 

[ballooza]

i'm so sorry i couldn't take place in such discussion because
I'm not an advanced physics student, yet. but at least i got
something to tell u, which is that Newton, as well as anybody
publishes a theory, found the essential formula of any system
including force. the whole process is about that he -somehow-
he derived that formula and applied it, and applications were a
100% correct, hence, that's enough for a proof because experiments
judge whether the formula and the concept is right or wrong. theories
could be updated,no doubt. As we see those space shuttles would've
never been applied if Newton's 2nd law was or will violated. and
that(space shuttles) i consider experimental proof says that it cannot be
violated. Logic is the judge of all, if human could just be 100%
logical thinking, human would be God, and wouldn't need experiments
as proofs.

 

[Antonio Lao]

InvariantBrian,

You have a good point.

When the quantum theory of the gravitational field was formulated, the quantum is the graviton. And proponents of this theory believe that graviton can act and react with itself. The graviton does act with anything that has a mass but this seems to work only with fermions. Since the graviton is a boson, I think it should also interact with other bosons. But most of the bosons do not have mass or do they? One of the unanswered questions is "what is mass?" Newton's three laws of motion and his universal law of gravitation all contain a mass factor.

Mass is a relational concept. Given one mass, we need another to compare it to. If the entire universe is one object, then it will have no mass.

Again, the old concept of the vacuum (empty space) has now been rejected by quantum theorists. They all believe the vacuum is not empty. It is composed of an infinite amount of virtual particles. The vacuum is not supposed to have any mass at all. But when virtual particles such as electrons and positron are produced they do have mass and energy. This is a puzzle to me.

Before the beginning of the big bang singularity, the universe is one whole object called the true vacuum, whose volume is zero but some sort of density is infinite.

 

[Antonio Lao]

which is that Newton, as well as anybody
publishes a theory, found the essential formula of any system
including force.

Newton's point-force mechanics has been superseded by analytical mechanics started by Lagrange, Euler, Bernoulli brothers, and many others in a mathematical physics known as the calculus of variations. These analyses put more emphases to energy functions than to functions of forces. The conjugate variables are the general momenta and positions and of course the time parameter.

 

[InvariantBrian]

Yes, but Newton's statements about forces are still correct even if there is a better way

 

[InvariantBrian]

all you have to remember is that Newton defines force as the change of momentum.
therefore the third law really states that momentum is conserved.

you could also say that third law in effect staes the net force acting on a closed sysem = 0

 

[Antonio Lao]

In physics, there are now known four fundamental forces. Not in any order of their singular discovery, these are the gravity, the EM force (Lorentz force), the weak nuclear force, the strong nuclear force.

The strength of these forces depended on the coupling constants found by experiments. Each of these constants are related to a scaled distance of effectiveness. The gravity and EM force are both long range forces, while the weak and strong are both short range forces. The force of gravity is the weakest of them all. But scientists believe that at extremely high energy density all these forces become equal in strength. The success of the unified electroweak force leads to the belief that we are on the right track. But somehow the energy scale is just not experimentally feasible.

In general relativity, the inertial force is equivalent to gravity. This is the principle of equivalence. Why they are equal remains a puzzle. But once the concept of mass is clearly understood, maybe, then and only then will we know the reason for the validity of this principle.

The common links between all these forces are two energy functions known as the Hamiltonian and the Lagrangian.

 

[InvariantBrian]

are you disagreeing with my statement that the definiton of force is the change of momentum

 

[Antonio Lao]

InvariantBrian,

No. But let me be more specific about it. In analytical mechanics, there are many ways that force is defined.

One definition is that force is the negative gradient of a scalar potential function.

F = -\vec{\nabla} V

This force depends only on the coordinates of the object to which the force is applied. It does not depends on the velocity of the object. And generalized forces can be defined as the derivative of the Lagrangian with respect to the generalized coordinates.

F_i = \frac{\partial L}{\partial q_i}

while the generalized momenta are given by

p_i = \frac{\partial L}{\partial \.{q}_i}

where \.{q}_i are the generalized velocities.

The first leads to Newton's 2nd law of motion.

 

[InvariantBrian]

I have no problem with what your saying. My only point is that Newton's third law is a genenal expression of the conservation of momentum if one remembers that force is defined as the change in momentum.

Newton's third law is still correct today in that general sense. Applying to in a modern way may call for some modification of this very general but important idea..agreed?

 

[InvariantBrian]

I'm mean...i guess your saying that force is defined many ways...fine...
but force as defined in Newton's laws of motion logically entails that the meaning of the third law..is a general expression of the conservation of momentum.

if force is defined other ways fine.

my point is that the third law is correct as it was defined by Newton...
that's all.

I...appreciate the discussion...

 

[Antonio Lao]

InvariantBrian,

I agree with what you said. But in almost all experiments of modern quantum physics, it is the change in energy that can be detected not so much as the force. While in classical mechanics, forces are disguised in all forms of vibrations and oscillations (damped or undamped). Although, We can still find the remnant of a direct application of the 3rd law in the science of rocket propulsions. But these necessarily need another law of conservation, the law of conservation of angular momentum besides the law of energy conservation.

There are really three major important laws of conservation.

1. Energy
2. linear momentum ( this is the one you are mostly concerned with, i guess).
3. angular momentum

Note: As a physical model, the 3rd law is very useful for linear systems. But, unfortunately, reality is mostly nonlinear. I could even say that it is really chaotic. But, the good thing is that the powerful energy principle is ideally applicable to all systems (linear or nonlinear or chaotic).

Energy (E) is just the "product" of force (F) and distance (d).

E = Fd

Vector analysis will help you understand the various ways of making a "product" of two vector quantities such as force and distance and velocity and linear momentum and angular momentum, etc.

 

[InvariantBrian]

My point is that Newton's third law is neither linear nor agular. It is general.
It states that generally momentum is conserved. And generally speaking, that is correct.

The third law is very simply stated:

action=reaction

and if one bears in mind that force is defined is at the change in momentum.

it follows that the third law genenally expresses the conservation of momentum.

It is a principle that can be used to derive the more specific laws of linear and angular momentum.

As a general statement, it is correct...in so far as it is generally true that momentum is conserved.

Does that makes sense?

Newton's laws were general principles he used to derive equations. The three laws themselves are not equations. They are used to derived equations.

 

[Antonio Lao]

InvariantBrian,

Once you are faced with an engineering problem, then you will start to realize that Newton's 3rd law is not enough to model physical reality. Specially in situation where static forces are in equilibrium, there is no obvious momentum because all velocity components are zero and hence all linear momenta are zero. In this particular case,
one cannot apply Newton's 3rd law directly. But forces still exist and they depend only on the coordinates instead of velocities.

 

[InvariantBrian]

InvariantBrian,

No. But let me be more specific about it. In analytical mechanics, there are many ways that force is defined.

One definition is that force is the negative gradient of a scalar potential function.

F = -\vec{\nabla} V

This force depends only on the coordinates of the object to which the force is applied. It does not depends on the velocity of the object. And generalized forces can be defined as the derivative of the Lagrangian with respect to the generalized coordinates.

F_i = \frac{\partial L}{\partial q_i}

while the generalized momenta are given by

p_i = \frac{\partial L}{\partial \.{q}_i}

where \.{q}_i are the generalized velocities.

The first leads to Newton's 2nd law of motion.

but that doesn't make Newton's second law wrong, force is
still always the change of momentum with respect to time in a system.
If that wasn't true once then that is the exception to Newton's second
law. In other words if we have moon orbiting a planet, then the gradient of
the potential is equal to the change of momentum with respect to time on
the moon.

 

[InvariantBrian]

InvariantBrian,

Once you are faced with an engineering problem, then you will start to realize that Newton's 3rd law is not enough to model physical reality. Specially in situation where static forces are in equilibrium, there is no obvious momentum because all velocity components are zero and hence all linear momenta are zero. In this particular case, one cannot apply Newton's 3rd law directly. But forces still exist and they depend only on the coordinates instead of velocities.

I agree. But Newton third law is a general principle that serves as a guide in solving particular engineering problems. As a guiding intuition regarding the general equilibrium of momentum, it is correct.

In fact it may be formulated this way...

The Third law in effect states the net force acting on a closed sysem = 0

 

[Antonio Lao]

but that doesn't make Newton's second law wrong, force is
still always the change of momentum with respect to time in a system.

Newton's 2nd is correct for all inertial forces wherever they exist in a system. But there are also other forces: gravitational forces, electrical forces, magnetic forces, frictional forces, weak forces, strong forces, electromagnetic forces, elastic forces,
molecular forces, atomic forces, van der Waals forces, and many other which do not depend on linear momenta.

The Third law in effect states the net force acting on a closed sysem = 0

But the momenta are zero although the forces are not. These are the forces that depended on coordinates instead of velocities. The key point to bear in mind is that there are two basic energies in mechanics: the potential and kinetic. The kinetic is derived based on the concept of work. This is the one that uses a force that is the change in momentum with respect to time in order to derive work integral. But if the work integral is zero then the system is conservative. This means the 3rd law is true.
There are also nonconservative systems to think about. For example the electromagnetic force, which depends on the concept of charge instead of mass as in all of Newton's laws.

 

[Antonio Lao]

InvariantBrian,

Bottomline is that in any given system, there are many forces of interaction between components. Whichever is the force that dominate the system, its law can be shown correct by experiments.

For the solar system, Newton's mechanics is correct because in this system, both the inertial force and the gravity force dominate.

For the atomic system, it is dominated by the electromagnetic force. There, Newton's forces are not quite applicable. They can be practically negligible in experiments.

For thermodynamic system, it is the heat energy that dominate the system although there are masses, the inertial forces derived from these masses can be neglected in formulating the kinetic theory of heat.

 

[InvariantBrian]

If the force is concervative in nature then that means that the
only thing that matters in regards to the work is the where you started
with regards to the center and how far from the potential you are when you ended. If it isn't, then the work on the system (if there is any) will depend on some other quantity. However, in ALL CASES ENERGY OF THE SYSTEM IS CONCERVED! In the case of the magnetic force (the electric is a concervative force), then the net work of the stystem is 0. However, Newton's third law still applies because the
derivative of the momentum with respect to time is a direvative of a
vector quantity, not a scaler.


For atomic systems the electric force dominates (although there
are things dealing with quantum mechanics) and yes, we still apply
Newton's Laws without issue. It is mathmatically NO DIFFERENT THAN A
PLANET (ignoring quantum mechanical effects such as spin and energy
splitting due to that, but then we don't deal with Newton's Laws in the
same way)

For a thermodynaic system the idea of "heat" is really simply that, an
idea. When we apply the kenetic theory of gasses we are forced to use
Newton's laws (ignoring quantum effects and doing it classically, of
course)

 

[Antonio Lao]

InvariantBrian,

Please check out the virial theorem and let me know why you think the potential is only half of the kinetic by using Newton's 3rd law? Thanks.

 

[InvariantBrian]

The viral theorm works with the kenetic energy being double the
potential for 1/r potentials only. The general expression of it is KE = PE/(1-n) where n is the power of the r. In fact, with a central potential Newton's third laws works great (gravity?!).

 

[Antonio Lao]

InvariantBrian,

I would say half not double. The reason for this is that given \alpha and \beta for what values will the following be true?

\frac{\alpha - \beta}{\alpha \beta} = 1

This is where \alpha = 1 is the potential energy and \beta = 1/2 is the kinetic energy. For higher positive values for both, the following must be graphed in the 1st quadrant.

\alpha = \frac{\beta}{1 - \beta}

and

\beta = \frac{\alpha}{1 + \alpha}

these graphs show that if one variable increases from 0 to infinity, the other asymptotically approaches unity. And if they are equal then they are both identically zero.

 

[Antonio Lao]

This general covariance of alpha and beta might be capable of explaining the factor of 1/2 in kinetic energy for the total energy of an isolated system.

E = \frac{1}{2} mv^2 + V

where V is the energy potential. In relativity, as v -> c, the energy is mc^2. The factor of 1/2 becomes unity.