The motion of falling objects is the simplest and most common
example of motion with changing velocity. The early pioneers of
physics had a correct intuition that the way things drop was a mes-
sage directly from Nature herself about how the universe worked.
Other examples seem less likely to have deep signi cance. A walking
person who speeds up is making a conscious choice. If one stretch of
a river ows more rapidly than another, it may be only because the
channel is narrower there, which is just an accident of the local ge-
ography. But there is something impressively consistent, universal,
and inexorable about the way things fall.
Stand up now and simultaneously drop a coin and a bit of paper
side by side. The paper takes much longer to hit the ground. That’s
why Aristotle wrote that heavy objects fell more rapidly. Europeans
believed him for two thousand years.
Now repeat the experiment, but make it into a race between the
coin and your shoe. My own shoe is about 50 times heavier than
the nickel I had handy, but it looks to me like they hit the ground at
exactly the same moment. So much for Aristotle! Galileo, who had
a air for the theatrical, did the experiment by dropping a bullet
and a heavy cannonball from a tall tower. Aristotle’s observations
had been incomplete, his interpretation a vast oversimpli cation.
It is inconceivable that Galileo was the rst person to observe a
discrepancy with Aristotle’s predictions. Galileo was the one who
changed the course of history because he was able to assemble the
observations into a coherent pattern, and also because he carried
out systematic quantitative (numerical) measurements rather than
just describing things qualitatively.
Why is it that some objects, like the coin and the shoe, have sim-
ilar motion, but others, like a feather or a bit of paper, are di erent?
Galileo speculated that in addition to the force that always pulls ob-
jects down, there was an upward force exerted by the air. Anyone
can speculate, but Galileo went beyond speculation and came up
with two clever experiments to probe the issue. First, he experi-
mented with objects falling in water, which probed the same issues
but made the motion slow enough that he could take time measure-
ments with a primitive pendulum clock. With this technique, he
established the following facts:
• All heavy, streamlined objects (for example a steel rod dropped
point-down) reach the bottom of the tank in about the same
amount of time, only slightly longer than the time they would
take to fall the same distance in air.
a / Galileo dropped a cannonball