
#91
Oct508, 10:01 AM

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#92
Oct508, 10:12 AM

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Now, the remainder of what you did is mathematically correct and leads to the trivially true assertion 0=0. This algebraic manipulation can be done for any formula. W = f.d W = W 0 = 0 x(t) = 1/2 a tē + v0 t + x0 x(t) = x(t) 0 = 0 Yes you can always do it, but in doing so you completely lose the meaning of the original expression. It looks like you are using the D'Alembert approach which can be useful in certain circumstances, but you need to understand what it is doing. Here is a thread on the subject. It should generally be avoided because of the conceptual confusion it causes, and it should only be applied when the specific problem demands it. In the end, if you are talking about inertial reference frames then ma is not a force and the body accelerates. If you are talking about the noninertial rest frame of an accelerating body (as D'Alembert does) then there is a fictitious inertial force (like the Coriolis force) of magnitude ma and the body does not accelerate. This force that exists only in the noninertial frame does not follow Newton's 3rd law because its source is the noninertial reference frame and not an interaction with another object. 



#93
Oct508, 10:16 AM

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#94
Oct508, 10:19 AM

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#95
Oct508, 10:23 AM

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By the way, none of this has anything to do with relativity, this is all just Newtonian mechanics. 



#96
Oct508, 03:23 PM

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Consider a two particle system: m_{1}, v_{1}, a_{1}: mass, velocity and acceleration of particle 1 m_{2}, v_{2}, a_{2}: mass, velocity and acceleration of particle 2 F_{12}: force on particle 1 due to the effect of particle 2 F_{21}: force on particle 2 due to the effect of particle 1 F_{12}=m_{1}a_{1} [E1: Newton's 2nd law for particle 1] F_{21}=m_{2}a_{2} [E2: Newton's 2nd law for particle 2] F_{12}=F_{21} [E3: Newton's 3rd law, action and reaction are equal and opposite] We can rearraange E3 as you did: F_{12}+F_{21}=0 [E3b] From E3 or E3b, neither F_{12} nor F_{21} is necessarily zero, only equal and opposite. From E1 and E2, assuming m_{1} and m_{2} positive and constant, F_{12} and F_{21} must be zero only if a_{1} or a_{2} are zero. But we can combine E3b with E1 and E2: F_{12}+F_{21}=m_{1}a_{1}+m_{2}a_{2}=d(m_{1}v_{1}+m_{2}v_{2})/dt=0, which says that there is no net force on both particles considered together (not separately) and that total momentum does not change over time, ie. momentum is conserved. 



#97
Oct508, 04:59 PM

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AM 



#98
Oct608, 03:47 AM

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nobody has addressed my very simple question. what about a hypothetical massless charged particle? it has self inductance so it would accelerate under the influence of an external field in exactly the same way that a massive particle would. the force due to self inductance exactly balancing the force due to the external field. net force is zero yet it still accelerates.
thats all I'm saying. I'm comparing the behavior of mass to the behavior of self inductance. as for defining force/mass, I can imagine a video game like universe in which time distance and velocity are all well defined but possessing nothing that we would recognize as force or mass. so I would guess that both arise simultaneously if the system possess some kind of symmetry. possibly related to conservation laws and Noethers theorem. I'm just guessing at this point. 



#99
Oct608, 04:16 AM

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Xiaochao Zheng's notes on "Radiation reaction and electron's self energy  an unsolved problem" http://www.jlab.org/~xiaochao/teachi...x/chap116.pdf 



#100
Oct608, 04:56 AM

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this hypothetical massless charged particle isnt a point change. it has finite diameter. and no I dont know whits holding it together. it doesnt matter. maybe superglue. 



#101
Oct608, 04:59 AM

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A particle with charge q in an electric field [itex]\vec E[/itex] experiences a force [itex]\vec F[/itex] = q[itex]\vec E[/itex]. The only thing that affects its acceleration is its mass. [itex]\vec F[/itex] = q[itex]\vec E[/itex] = ma. There is no other force. AM 



#102
Oct608, 05:04 AM

P: 2,258

whoa. a moving charge has energy in its magnetic field. this energy must be supplied by the external force. it would not move at the speed of light. 



#103
Oct608, 05:45 AM

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Jammer, Concepts of Mass, Chapter 11 http://books.google.com/books?hl=en&...sult#PPA136,M1 Accelerationdependent selfinteraction effects as a possible mechanism of inertia Vesselin Petkov http://arxiv.org/abs/physics/9909019 



#104
Oct608, 12:57 PM

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A charged particle cannot move at the speed of light because all particles with charge have mass. Light will always travel at the speed of light, c, relative to a particle with mass. The only inertia, or resistance to change in speed, of a charged particle in an electric field is due to the mass of the charged particle, as explained in my previous post. (At relativistic speeds, the apparent inertia increases due to relativistic effects). AM 



#105
Oct608, 04:45 PM

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References that seem to be regarded as standard, but not available for free are: A.D. Yagjian, Relativistic Dynamics of a Charged Sphere, 2nd ed. Springer 2006 F. Rohrlich, Classical Charged Particles, 3rd ed. (World Scientific 2007) On arXiv: Radiation reaction of a classical quasirigid extended particle Rodrigo Medina http://arxiv.org/abs/physics/0508031 



#106
Oct608, 04:55 PM

P: 2,258

it doesnt need to be possible. its hypothetical. I'm not suggesting that mass really is due to self induction. I'm saying that one can look at it in the same way.
lorentz spent a good deal of energy looking for a way to make mass be due to self induction. so apparently he didnt think it was an impossible idea. 



#107
Oct608, 04:58 PM

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#108
Oct708, 06:26 PM

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Self induction is a phenomenon that occurs in a coil due to current flow. The expanding magnetic field from increasing current in one coil cuts across an adjacent coil and induces a current that opposes the increasing current. Electrons do not experience self induction. You seem to be suggesting that there is something other than mass that causes a charged particle to resist changes in its motion. AM 


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