----- The following copyright 1991 by Dirk Terrell
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 Lecture #3  "On the Move"

   Now lets' see how the scientific method and mathematics were applied to 
the study of motion, sometimes referred to as 'mechanics'. One schoool of 
thought, headed by Aristotle, held that the natural state of matter was 
rest, objects in motion would naturally come to rest. It is easy to see why 
this conclusion was held for so long. A ball that is sitting still will not 
spontaneously start rolling. Also, a ball that is pushed will roll, but 
eventually it will come to a rest. Aristotle's hypothesis predicts that the 
ball, when pushed, will come to rest. Observations show that to be true. 
Therefore, Aristotle's hypothesis is proven. Right? Wrong! Remember, a 
hypothesis can be SUPPORTED by experiment, never PROVEN. But the experiments 
backed up Aristotle's hypothesis and thus it became the theory of motion 
that was used for quite a long time. 

   Galileo Galilei was, perhaps, the first experimental physicist. He 
pioneered the use of carefully made measurements to test hypotheses. He 
showed that the time it took for a pendulum to complete one swing (the 
period) depended only on its length, not on how far it traveled (the 
amplitude). These studies led to the development of pendulum clocks. His 
interest in pendulums led him to study the motion of projectiles by 
splitting the motion into two parts - vertical and horizontal. He studied 
the motion of balls rolling down inclined planes which approximated vertical 
motion, but enabled him to make more accurate measurements because the 
motion was slower.

   Let's look a little more closely at Galileo's inclined plane experiments, 
and let me encourage you to do them yourself. How long does it take for 
something to fall a certain distance? Another way of asking the same 
question is how does the distance fallen depend mathematically on the time 
duration of the fall? Galileo predicted that the distance fallen would 
depend on the SQUARE of the time. That is, if a ball fell 10 feet in one 
second, in two seconds it would fall two squared, or FOUR, times as far - 40 
feet. His experiments showed that his prediction was correct. He also found 
that the speed of the ball increased in a uniform way. At the end of one 
second the ball might be moving one meter per second. After two seconds it 
was moving two m/sec. After 3 sec it was moving 3 m/sec. Mathematically we 
would state this observation as the speed was proportional to the time of 
fall. Let us write these findings as mathematical equations:

     let 's' be distance, 'v' be speed, and 't' be time
        s | t*t  or s | t^2
     and 
        v | t 
     where the symbol '|' means 'is proportional to'

   Galileo also found that the above findings did NOT depend on the mass of 
the ball- a heavy ball had the same properties as a light ball. This finding 
manifests itself in the stories you may have heard of Galileo dropping items 
of different weight from the Tower of Pisa. I'm not sure if the stories are 
true. Now, this is probably the first thing I've said that doesn't match up 
to what your common sense is telling you. What I'm saying is that a feather 
and a bowling ball will fall at the same rate! But that's not what happens, 
is it? So what gives? Galileo discovered that objects resist a CHANGE in 
their motion. If they are at rest, they tend to stay at rest. If they are in 
motion, something must act on them to slow them down. For falling objects 
near the surface of the earth, air tends to resist their motion. Some 
objects are affected more by air resistance than others. The feather will be 
slowed more than the bowling ball, and hence it falls more slowly. We could 
test this hypothesis by dropping objects in a vacuum. Apollo 15 Commander 
Dave Scott did this on the surface of the moon by dropping a feather and a 
hammer. They both hit the surface of the moon at the same time. 

   The fact that Galileo was able to take measurements of objects affected 
by friction and air resistance and extrapolate them to a regime of no 
friction says something about his physical intuition and mathematical 
skills. Unfortunately, Galileo's support of the Copernican theory of the 
solar system, so stated in his book "Dialogo dei Due Massimmi Sistemi" 
(Dialogue on the Two Great World Systems), put him on a collision course 
with the Roman Catholic church, which stated that the earth, not the sun, 
was the center of the sun. Even though he was tried for political and 
religious reasons, he was forced to publicly recant his scientific views, 
and he spent the last years of his life under house arrest. The church was 
able to silence Galileo, but as we shall see, the investigation of nature 
cannot be stopped by censorship. In fact, in 1983 the Roman Catholic 
re-opened the case against Galileo and admitted that it had erred. Galileo's 
name was cleared after 350 years. I cannot help but think of Galileo when I 
hear religious arguments against evolution. I wonder what the church's 
position on evolution will be 350 years from now? Dirk