A Non Fiction Trilogy

APPENDIX B           MOTION WITHIN MASS AREAS


           

          If we consider the established notion of impenetrability the result occurs, that either:


            1.   Impact is not possible or,

            2.   Motion transfer is instantaneous


         As to the question of having two motions in the same instant, Jammer describes Boscovich’s words: “…it would amount to saying that the body would be bound to have 12 degrees of velocity and 9 at one and the same instant”.1

            Boscovich therefore concluded that impact was illogical and proceeded to use forces to describe changes in motion (impulse). Others accepted the notion of instantaneous transfer motion2.

            I concur with the later as having two velocities to a body at the same instant only follows from what the concept of an instant is, that is (analogous to mathematical points and area) it is not an interval of time but the separation point of time intervals.   So the first velocity occurs up until that instant (of contact) and the second velocity occurs after that instant.

            Therefore there is no reason to suppose instantaneous transfer of motion is not possible.

Further Considerations


Points of Contact

            

            For rod contact as described in chapter 2, here the contact between two rods have an area = zero. This point of contact on the two rods, or any point of contact of two areas or lines, is the same point (Principle I-1, See Appendix I). This seems odd as the two rods have a outer "point" for each, but when they come together it becomes the same point. But this is so, as that point is just a defining measure, what was the separation of mass area with non-mass area (unoccupied space), becomes, as the gap is closed, the separation point of the two masses.  


Instantaneous Motion


           So, the quality of motion (momentum) must “pass through” a point of zero area.   So, if only for an instant, momentum must move in one dimension.   As mass is decreased the velocity becomes infinite, however, in my opinion, the quality/quantity, even at infinite velocity remains as the original v x m factor.   So that when motion is given back from a mathematical point to a mass area the proportion is v x m : v1 x m1 again.

            But the idea remains that motion has been accounted the property of traveling through a mathematical point (if the proposition of motion rod to rod is accepted).   Furthermore if 2 rods are brought to contact along their lengths we have a line of contact with no area and momentum must be transferred instantly along this one dimensional line also.   And since mathematical points and lines separate areas of mass that are in contact anywhere in a mass area, then momentum can be transferred from any part of a mass area to another instantly. So I consider motion is transferred instantly within a rod or between two rods in contact. 

         

1 Jammer, Max, Concepts of Force, A Study in the Foundations of Physics, Harvard University Press, Cambridge, Mass. 1957, p. 172

2 Scott, Wilson L., The Conflict Between Atomism and Conservation Theory 1644 to 1860, Elsevier/MacDonald, 1970.General in book.



>Appendix C A Calculation of Transfer of Rotational Motion