Re: kinematics, traditional or not

[Tim Folkerts <tfolkert@FHSU.EDU>]

> Indeed in relativistic conditions, F=ma no longer holds.
> You can patch things up by redefining F ... or by redefining
> a.  And in fact people really do redefine v and a!  We redefine
>    v = (d/d tau) x                 (1)
>    a = (d/d tau) v
> instead of
>    v ?= (d/d t) x                  (3)
>    a ?= (d/d t) v
>
> and the relativistic momentum is p=mv using the v from
> equation (1) not equation (3).

I was hoping to avoid relativity because I am not an expert and I'm not up
on current pedagogy, but...

If I say an electron has "a speed of 0.999c", I think I mean that the
electron will move a distance of 299,792,458*0.999 meters (by my
meterstick) in one second (by my watch).  I don't see why I need to
redefine v.  It seems I am still using v==dx/dt.  Sure, someone in a
different frame will get a different answer, but that is true even in
Galilean transformations.

Certainly, F <> ma in the Newtonian sense.  I would tend to look to F =
dp/dt.  Then I would say that applying a force (say from a uniform E) to an
electron that becomes highly relativistic means:
   Force is constant
   speed approaches c
   acceleration approaches 0 (since the speed mostly stops changing)
   a = F/gamma*(rest mass)
   momentum continues to increase linearly:  dp = qE dt

Is this not a reasonable way to view things?  I would keep the gamma
explicit, rather than bury it in either m or v or t.

Tim Folkerts


Department of Physics
Fort Hays State University
Hays, KS  67601
785-628-4501