# Newton's Third Law

## Main Question or Discussion Point

I have heard that newton's third law fails to apply in certain cases.
Is it true??
and if it is , is there a reason why it works in the remaining cases?

also regarding the second law F=dp/dt
is it how force is defined ??or is it a relation between force and change in momentum??
if it is how force is defined, then newton's second law cannot be wrong..

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Hi there,

Newton's laws (the three of them) are defined for system of particles in motion, but at very low speed (compared to the speed of light). Therefore, Newton's laws are not wrong, but they are an approximation of the truth, for which the deviation is so tiny that we can't see it at Earthly velocities.

As soon as you are in a system where relativistic effects become visible, then you notice the deviation from the approximation.

In reality, Newton was completely right, expect for one major detail. He assumed the mass of an object to be constant. Which we know now that the mass of an object is dependent on the speed of it's reference frame.

For the second law equation:$$\vec{F} = \frac{d\vec{p}}{dt}$$ is completely right. The approximation comes in the motion quantity: $$\vec{p}$$ which Newton said to be: $$\vec{p} = m \frac{d\vec{r}}{dt}$$ To be completely right, Newton should have written his equation: $$\vec{p} = \frac{d(m \vec{r}}{dt}$$

1.Can you be more specific about where you think the third law fails?
2.It is both.Experiment shows that the rate of change of momentum is proportional to the resultant force and one Newton can be defined as the resultant force that gives a mass of one kilogramme an acceleration of one metre per second squared.

arildno
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Gold Member
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You need not go to relativistic physics in order to find violations of the 3.law.

In classical physics, the 3.law is only generally valid for CONTACT forces, whereas for a force-acting-on-distance like the magnetic force, it is not valid to assume that the action-reaction couple of forces sum to 0.
They don't.

Yet, even in this case in classical physics, we have conservation of momentum of the system, but some of that momentum is embedded in the electro-magnetic field set up by two charged particles; i.e, the sum of the particle's momenta is not conserved (as would be the case if the action-reaction force couple betweeen them summed to zero)

You need not go to relativistic physics in order to find violations of the 3.law.

In classical physics, the 3.law is only generally valid for CONTACT forces, whereas for a force-acting-on-distance like the magnetic force, it is not valid to assume that the action-reaction couple of forces sum to 0.
They don't.

Yet, even in this case in classical physics, we have conservation of momentum of the system, but some of that momentum is embedded in the electro-magnetic field set up by two charged particles; i.e, the sum of the particle's momenta is not conserved (as would be the case if the action-reaction force couple betweeen them summed to zero)
Interesting and I would be grateful if you could tell me more.I have already searched similar threads on this forum and I have googled but opinion seems to be divided.I can see,I think,that if you make changes,say to a magnet, at one place then there will be a delay for these changes to be felt at another place but what happens when a sort of equilibrium is reached?My gut feeling is that that the action reaction forces average out over time to equal values but display some sort of quantum fluctuations due to the finite time for the signals to travel.I am particularly interested by how you can prove,by experiment,the supposed violation of the third law(or indeeed its universal validity).

There are some cases in electromagnetism which are usually discussed as situations when the third law is not valid. It's classical not relativistic (if EM can be called classic).
I have to look them up, I don't remember now. I thing that the forces (action and reaction) are not opposite in directions.

i got one i think,
i can't draw it, but try to get it through descriptions
imagine the two dimensional co-ordinate axis.
At a particular instant:
charge q1 at the origin, moving with v1 velocity towards +ve x axis
charge q2 at (0,d) (on y axis) moving with v2 velocity towards +ve y axis.

as far as i have calculated, newton's law fails, as q2 does not exert a magnetic force on q1 but q1 does exert a magnetic force on q2

is it correct to infer??

fatra2 wrote:

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Newton's laws (the three of them) are defined for system of particles in motion, but at very low speed (compared to the speed of light). Therefore, Newton's laws are not wrong, but they are an approximation of the truth, for which the deviation is so tiny that we can't see it at Earthly velocities.
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This is a common statement, but it is not quite right. What we call the "magnetic field" -- the magnetic lines of force which encircle a wire which is conducting a current -- is a relativistic effect due to the relative motion of the electrostatically charged electrons. These electrons have a drift velocity of about one foot per hour. The relativistic factor 1/(1 - v^2/ c^2) where v equals *only 1 foot per hour* gives rise to the macroscopic magnetic field. Why? Because Avogadro's constant is 6.02 * 10^23. All those infinitesimal relativistic effects add up, electron by electron, to effect the macroscopic magnetic field. Relativity does not manifest itself only at high speeds.

Sorry, I meant to write 1/(sqrt(1 - v^2/c^2)

diazona
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i got one i think,
i can't draw it, but try to get it through descriptions
imagine the two dimensional co-ordinate axis.
At a particular instant:
charge q1 at the origin, moving with v1 velocity towards +ve x axis
charge q2 at (0,d) (on y axis) moving with v2 velocity towards +ve y axis.

as far as i have calculated, newton's law fails, as q2 does not exert a magnetic force on q1 but q1 does exert a magnetic force on q2

is it correct to infer??
Yep, that sounds right.