Re: kinematics, traditional or not

[Tim Folkerts <tfolkert@FHSU.EDU>]

Joe Heafner said a couple things that I'd like to comment on, because they
seem a bit backwards to me.

> I had in mind the usual way in which the 5 (?) equations of kinematics
> are usually derived from F=ma with the assumption of constant
> acceleration.... It seems a better approach would be to start with
> dynamics in general, and then show how traditional kinematics is
> merely a very special (albeit sometimes useful) case.

> The traditional textbook kinematics can be improved by showing how
> that approach is merely a special case of F=dp/dt. Students need to
> see the big picture before they see a limited view.

I don't view kinematics as derived from dynamics, or as a special case of
F=ma.

The kinematic equations are merely mathematical definitions.  After
DEFINING
v==dr/dt and a==dv/dt , you can use calculus to DERIVE  x = 1/2at^2 +
v(0)t+ x(0), etc for constant acceleration, or DERIVE a = v^2/r for
circular motion.  This has nothing to do with forces.

F = ma is a much deeper statement.  You can determine mass; you can
determine acceleration; you can determine force.  It turns out that,
EXPERIMENTALLY, F=ma.  There is nothing that a priori requires this
particular relationship, it just happens that there is such a nice, simple
relationship in the universe.  It is conceivable that an experiment might
disagree with F=ma and that it would have to be modified.  But I don't see
how you could change a==dv/dt==d^2r/dt^2.

F/m is NOT acceleration, its force/mass.  That this is numerically equal to
acceleration is a terribly useful, but I don't agree with using this to
derive kinematics.  (I haven't seen "Matter and Interactions", so I can't
comment on just how they handle this.)


Tim Folkerts



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