As most good sophomore engineers, Manuel had enrolled
in the introductory mechanics course at The Ohio State
University. Manuel was a good student with a strong
background in mathematics and so he had little problem
drawing free body diagrams, writing down Newton's Laws,
and solving them for forces and accelerations. Being
somewhat more clever than the average sophomore engineering
student, Manuel wanted to know more. Manuel wanted to
know why. And so Manuel arrived at the inevitable
conclusion. He would have to climb the mountain of
stairs to the 11th floor of Boyd Lab and confront the
Mechanician. He would not leave until the Mechanician
revealed to him the secret of Mechanics.
When he reached the 11th floor, Manuel knew he had made
the right decision. Adorning the hall were pictures of
of all the great Mechanicians, past and present. There
was Kepler, and Pascal. Ah, and there was Bill Hamilton
and over there was LaGrange. Yes this was the place all
right.
At the end of the hall was Sir Isaac himself and next to
his picture, the office of the Mechanician. Manuel barely
noticed the sign on the door,
Conserve Angular Momentum
Keep this Door Closed!
as he tentatively knocked. Manuel thought he heard a faint
shuffling from behind the door followed by what seemed to
be a crash of books to floor and a muffled curse. The door
finally opened, "Yes, what is it?". "Sir, I have a few
questions" said Manuel softly. The Mechanician replied
"Oh very well" making a point of removing his pocket watch,
glancing at the time and then placing the watch in plain view
on his desk. "What is it?".
Following is the conversation between Manuel and
the Mechanician.
# = Manuel; % = the Mechanician
#Sir, I am doing quite well in your course even though,
#well, err, ....
%Quit your stammering young man, out with it already.
#Well, even though you haven't actually attended class
#yet. But I'm sure you're very busy with the deeper things
#of mechanics, and your grad assistant is really doing
#a marvelous job.
%Ah yes, very well then. So you are doing well, what's
%the problem then? Oh, you don't want to take the final,
%is that it?
#No no! I want to go deeper. I can calculate forces and
#accelerations but I don't know what these things mean.
#Suppose I have a particle with a force acting on it.
#What is this force, it seems rather abstract to me.
%I see, well, the force acting on a particle is the time
%derivative of the linear momentum. If the mass is constant
%then the force is the mass times the acceleration.
#Yes, we are just starting to talk about the linear momentum
#class. What is it exactly?
%mass times velocity.
#This is not particularly useful, er, I mean... Can you
#explain it in some other way.
%The linear momentum is that quantity which, when differentiated,
%gives the force.
#And what is the force again?
%Its the time derivative of the linear momentum, weren't you
%listening? <glancing at his watch>
#Uh, well, ... I understand this linear momentum is conserved
#in some situations. Why?
%No one knows.
#I see, well, this mass business seems important. What is the
#mass anyway?
%The mass is a quantitative measure of the inertia of a body.
#What is this inertia?
%It is a measure of the resistance of a body to a change in its
%motion. A body in motion will continue in motion along a
%straight line unless acted on by a force. A body at rest
%will remain at rest unless acted on by a force.
#Now we're getting somewhere. The reason it takes a force to
#get something moving is because all bodies have inertia.
%No, no. You misunderstood. Inertia is just a name, kind of a
%shorthand, that we give to this observation that all bodies
%display a resistance to a change in their motion.
#Okay, so why do all bodies have this property of inertia?
%No one knows.
<At this point, it was Manuel who looked at the Mechanicians
watch>
#Sir, it is time for class. Will you be there today?
%I think not.
Manuel, remembering Descartes, was somewhat disappointed that
the Mechanician did not vanish into thin air.
Actually, Manuel didn't go to class that day. Instead he went
straight to his guidance counselor and changed his major to
Basket Weaving. On the way some heard him muttering about
forces and momentums and inertia and about mechanics being
a meaningless string of tautological statements.
===========================
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"Should I refuse a good dinner simply because I
do not understand the process of digestion?"
-- Oliver Heaviside