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I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION and they say that Newton's 3rd law only applies when forces are $\textbf{central forces}$, basically if the force of one particle onto another is directed along the line connecting the objects.

$\textbf{Question 1}$

for collisions, eg: 30cm ruler and a golf ball; if the golf ball strikes the ruler at 25cm mark, then the "line connecting" the object is for each of the particles in the golf ball that collide with a particle in the ruler and not line from golf ball to line to ruler?(green circles are ruler particles and purple circles are particles in golf ball) enter image description here

Basically "line connecting" does not mean connecting to center of mass of the object body unless the objects are points?

$\textbf{Question 2}$

They say, "Any force that depends on the velocities of the interacting bodies is noncentral" But aren't all collisions velocity dependent, thus making collisions noncentral? For 2 objects traveling toward each other, increasing their speeds will increase the amount of force the objects have on each other. People also you drag as an example of forces that are velocity dependent, but isn't that essentially the same thing as objects colliding with each other just that the objects are gas/liquid molecules

$\textbf{Question 3}$

they say, " Velocity dependent forces are characteristic of interactions that propagate with finite velocity." then they give an example with moving electric charges, "the force between moving electric charges does not obey the 3rd law, because the force propagates with the velocity of light"

First what does "$\textit{interactions that propagate}$ with finite velocity" and "$\textit{force propagates} $ with the velocity of light" mean? Are they saying that force (magnetic field) originates from the charged particle and travels(propagates) outward at finite speed, in this case the speed of light?

But now we have a problem, they say gravitational force is a central force, but its force(gravitational field) also originating from the object as propagates outward at finite speed, with the exception that it's force is not velocity dependent.

Unless I have got this totally incorrect, I then think that the 3rd law does not apply if the force is $\textbf{both}$ velocity dependent and that it's $\textit{interactions that propagate}$ at finite speed (basically a time/distance delay between the 2 objects) as:

  • Gravitational force: propagates at finite speed but not velocity dependent(Thus 3rd law applies)
  • Collisions: velocity dependent but not instantaneous(Thus 3rd law applies)
  • Magnetic force: propagates at finite speed and velocity dependent (Thus 3rd law $\textbf{not}$ apply)
  • Electrostatic force: propagates at finite speed but not velocity dependent(Thus 3rd law applies

I have been struggling to find a clear answer to these questions but I only manage to get little bits on information here and there and I would like to be able to see the big picture. I would really appreciate any answers you can give to add some light to my problem

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    $\begingroup$ If you view Newton's third law as stating that the total moment of of a system is always conserved, then I believe it is applicable to your third bullet . See quora.com/…. $\endgroup$
    – Bob D
    Commented Jan 12, 2022 at 15:22
  • $\begingroup$ @BobD ok thanks and would you say in general my reasoning is correct or is there still something I am not getting? $\endgroup$
    – Reuben
    Commented Jan 12, 2022 at 17:21
  • $\begingroup$ Newton's third law can't be violated by any conditions. That's all. $\endgroup$
    – Debanjan Biswas
    Commented Sep 7, 2022 at 17:40
  • $\begingroup$ Could you cite the specific passage in Thornton & Marion where they say this? I'd like to see context. I own a copy of the book, so no need to transcribe it for me. $\endgroup$
    – Logan J. Fisher
    Commented Jun 4, 2023 at 21:32

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