Re: Kinematics First

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

At 7:54 AM -0500 9/17/02, Rick Tarara wrote:

> I just don't see how you can introduce Newton's Laws successfully if
> students don't understand ACCELERATION.  ...

In recent years I've been going around spouting off my own perhaps
marginally hyperbolic observation that Newton himself didn't
understand acceleration.  I believe that a careful reading of the
Principia will reveal that Newton never got very far beyond the idea
of impulse and momentum.  Newton's second and third laws are
explicitly about impulses ("action" to Newton) and changES in
momentum ("motion" to Newton), NOT forces and changING velocity--a
subtle but critically important distinction IMO.

Accordingly, I have been a strong advocate of "Force First."  In this
program students begin with statics (as was almost universally done
years ago) and learn about vectors in a much simpler context using
relationships that involve only one kind of vector (i.e., forces)
rather than two kinds of vectors with one of them being multiplied by
a scalar (i.e., F=ma).

After we know how to deal with situations in which F_net = 0 (and see
from simple examples that they include not just v = 0, but also v =
constant), we ask what happens when F_net does NOT equal 0.  The
answer is that v changES.  We argue straightforwardly that the amount
of change should depend directly on the size of the unbalanced force
and the amount of time that that unbalanced force acts and inversely
on the mass of the object and immediately have Newton's second law in
the form that Newton gave it (i.e. F delta t = m delta v).  Moreover,
we take advantage of students' natural tendency to believe that when
we throw a stone the effect of our throwing "lasts" even after the
stone leaves our hand.  It does, of course; our hand supplies impulse
and that impulse lasts in the form of its acquired momentum.

Finally, we notice that, if the velocity changES between the
endpoints of some interval of time, then it must have been changING
DURING that interval of time.  At that point we simply go to the
differential form of Newton's second law and writing F dt = m dv =>
dv/dt = F/m and, for the FIRST time utter the word "acceleration."
At that point students are far better prepared to talk about and
distinguish between situations in which the force is constant, or
dependent on position (e.g., simple harmonic oscillation), or on
velocity (e.g., viscous drag), or time.  They aren't led to believe
as so many do with current instruction that "acceleration IS
constant."

Admittedly, I have not yet written "my book" and have not, therefore,
had the opportunity to properly test this program.  But I believe it
offers tremendous advantages over the traditional program precisely
because it delays any discussion of acceleration to the very end of
the mechanics section.

John
--
   A. John Mallinckrodt        http://www.csupomona.edu/~ajm
   Professor of Physics      mailto:ajm@csupomona.edu
   Physics Department         voice:909-869-4054
   Cal Poly Pomona              fax:909-869-5090
   Pomona, CA 91768-4031     office:Building 8, Room 223