Newton's Laws 2020

Newton’s laws: ( From the book “Revenge of the Sinister Universe” )

     In this blog post we present a synopsis of the ‘universal’ formulation, or expression, 

     of Newton’s laws, as proposed in our book, “On Rotation”.

     [This formulation is good in any reference frame.]

     Newton’s first law:

     If a particle does not experience a change in angular momentum

relative to any arbitrarily chosen point in the universal reference frame,

then the particle is considered to be free 

(i.e. there are no net forces acting on it).

     For a two body system, if there is no change in the angular momentum

of either body comprising the two body system relative to any arbitrary point

(this ‘excludes’ the choice of points lying along the unit vector, r),

then the particles are not interacting.

     Newton’s second law:

     A particle that undergoes a change in angular momentum relative to our arbitrarily chosen
point (i.e. the origin of our coordinate system) is said to experience a net torque, τ;

     τ =  dL/dt  =  rxF                                                                            (a)

where the force, F, is defined by 

     F = dp/dt  =  d(mv)/dt  =  m dv/dt  +  v dm/dt                                    (b)

.

     For two body ‘central force’ motion, the torques experienced by each individual body 

relative to our chosen reference point, are equal and opposite;

     r1xF1  = -r2xF2        ;   |F|  =  |F1-F2|                                                     (c)

                                                              ⇔

     Newton’s third law:

     During a two body interaction, the two bodies will undergo equal and

opposite changes in their respective ‘actions’; i.e. they will have equal,

and ‘opposite’, changes in kinetic energy.

    δ∫dL/dt ωdt  =  0                                                                              (d) 

where           

     τTOTAL  =  τFORCE + τSPIN                                                            (e)

and 

     τSPIN  =  I1 x B2 + I2 x B1                                                                      (f)

     Newton’s universal law of gravitation, expressed in the center of mass of a two body system,
becomes;   

     F/ETOT =  K*(c/R)2 -  K*(v2/R2)  -  K*(l2/R3)                                    (g)

     K  = (μ_0/4π) G/c2                                                                        (h)

where the second term on the right hand side of equation (g) is the Coriolis force; our answer to spacetime disturbances.  [This extra term will describe the rotation of
galaxies without the inclusion of ‘dark matter’; and the perihelion of the planet Mercury.]

[For galaxy rotation, one must include the ‘relativistic’ mass of the individual bodies due to spin.]

Since our new Coriolis force term goes as 1/R2, the classical and quantum mechanical     
conservation of the first three integrals of the motion, E, L, Lz, is still guaranteed.