The Feather and the Penny

Extracting a simple law of physics from a set of measurements is not so simple.  Nature hides the simplicity in a thicket of complicating circumstances, and the experimenter’s job is to prune away these complications.  The law of free fall is a splendid example.   In freshman physics we hold a feather and a penny at the top of a tall glass tube and drop them simultaneously.  The penny falls rapidly and clinks to the bottom in less than a second.  The feather floats gently down, arriving in five or six seconds.  Such observations led Aristotle (384 BC – 322 BC, a student of Plato) to postulate his law that heavier objects fall faster than light ones.  Now we pump the air out of the tube and repeat the experiment.  Feather and penny drop with equal times.  Air resistance obscures the law of free fall.  To make progress, we must remove this complicating feature to get the simple law.  Later, if it is important, we can learn how to add this effect back in to arrive at a more complex but more applicable law.

The Aristotelians believed that an object’s  “natural” state was to be at rest.  Push a ball along a plane and it comes to rest, no?  Galileo knew all about  imperfect conditions, and that understanding led to one of the great discoveries.  He read physics in inclined planes as Michelangelo saw magnificent bodies in slabs of marble.  He realized, however, that because of friction, air pressure, and other imperfect conditions, his inclined plane was not ideal for studying the forces on various objects.  What happens, he pondered, if you have an ideal plane?  Like Democritus (ca. 460 BC – ca. 370 BC) mentally sharpening his knife, you mentally polish the plane until it attains the ultimate smoothness, completely free of friction.  Then you stick itin an evacuated chamber to get rid of air resistance.  And you extend the plane to infinity.  You make sure the plane is absolutely horizontal.  Now when you give a tiny nudge to the perfectly polished ball sitting on your smooth, smooth plane, how far will it roll?  For how long will it roll? (As long as all of this is in the mind, the experiment is possible and cheap.)

The answer is forever.  Galileo reasoned thus:  when a plane, even an earthly imperfect plane, is tilted up, a ball, started by a push from the bottom, will go slower and slower.  If the plane is tilted down, a ball released at the top will go faster and faster.  Therefore using the intuitive sense of continuity of action, he concluded that a ball on a flat plane will neither slow down nor speed up but will continue forever.  Galileo had made an intuitive jump to what we now call Newton’s first law of motion: a body in motion tends to remain in motion.  Forces are not necessary for motion, only for changes in motion.  In contrast to the Aristotelian view, a body’s natural state is motion with constant velocity.  Rest I s the special case of zero velocity, but in the new view that is no more natural than any other constant velocity.   For anyone who has driven a car or a chariot, this is a counterintuitive ideal. Unless you keep your foot on the pedal or keep whipping the horse, the vehicle will halt.  Galileo saw that to find the truth you must mentally attribute ideal conditions to your instrument.  (or drive your car on an ice-slicked road.)  It was Galileo’s genius to see how to remove natural obfuscations such as friction and air resistance to establish a set of fundamental relations about the world.