# Galileo gets balls rolling and squares his theory

Thu, Jan 17, 2013, 00:00

OPINION:The work conducted by the father of modern science played a major role in developing human thinking, writes WILLIAM REVILLE

Galileo Galilei (1564 – 1642) is best known for his trial by the Roman Inquisition, which found him “vehemently suspect of heresy” for advocating a sun-centred solar system. But, perhaps Galileo’s main claim to greatness resides in work he carried out long before he quarrelled with the Vatican, when he studied the laws governing how simple objects move. This work is elegantly described by George Johnson in his book The Ten Most Beautiful Experiments (The Bodley Head, 2008).

Aristotle (384 BC-322 BC) was the first to make a determined attempt to describe the rules of motion. He said that objects fall at rates proportional to their weights – if you simultaneously drop a hammer and a nail, the hammer will hit the ground first. (It always intrigued me why he never checked this out practically.)

Aristotle’s ideas make intuitive sense, but they’re wrong and Galileo comprehensively demonstrated this. In his masterpiece publication, Dialogue Concerning the Two New Sciences (1638), he described an experiment in which a 100-pound cannonball and a one-pound musket ball are dropped simultaneously and both hit the ground at almost the same time. The cannon ball hit the ground ever so slightly before the musket ball, landing by “two finger breadths sooner”. However Galileo recognised that other factors, such as air-resistance, accounted for the tiny difference. Aristotle predicted that the cannon ball would hit the ground long before the musket ball.

Galileo concluded that, all other things being equal, the rate of fall of an object is independent of its weight. All objects fall at the same rate in a vacuum and the lunar astronauts demonstrated this on the moon in 1971, dropping a feather and a spanner which hit the ground simultaneously.

But what about the motion of a falling object between its release and hitting the ground? Obviously the rate of descent increases along the way, but in what manner? Does it make a spurt at the start and then maintain a constant speed, or does it smoothly increase speed all the way down? Bodies fall very quickly and Galileo did not have technical devices such as time-lapse photography to study the phenomenon. So, he decided to slow down the falling process in order to time it with devices available to him.

Galileo decided to study balls rolling (falling) down smooth inclined planes. He reasoned that what is true for a gentle incline is true for a steeper incline and so on up to the steepest of all inclines – straight-down free fall. Galileo took wooden boards, about 20 feet long, along which he carved straight smooth channels. He then timed how long it took a bronze ball to roll down the channel with the board set at different slopes. Measurements were also made of the time the ball took to traverse different fractions of the total length of the channel – ¼, ½, ¾, etc.

Galileo divided the time of descent into equal intervals (“ticks”) and measured the length of the descent (length of track traversed) in numbers of equidistant “points” on a ruler. The following figures record a typical experiment in Galileo’s notebook (the first number in each pair of numbers is the number of elapsed ticks of time and the second number is the accumulated distance at that time in points): 1, 33; 2, 130; 3, 298; 4, 526; 5, 824; 6, 1192; 7, 1620; 8, 2104.

Galileo analysed these numbers and unveiled a pattern as follows. If you divide 33, the distance covered on the first tick, into each of the distances travelled on the eight ticks you get the following sequence 1, 3.9, 9.03, 15.9, 25, 36.1, 49.1, 63.8. Rounding out the numbers you get one squared, two squared, three squared, four squared, five squared, six squared, seven squared and eight squared.

Allowing for some experimental error, the distance covered is directly proportional to the square of the time. An object in free fall for two seconds drops four times the distance it drops in one second, and in three seconds it drops nine times the one-second distance, and so on. This is Galileo’s Law of Falling Bodies.

Galileo is rightly called the father of modern science. He was one of the first to clearly state that the laws of nature are mathematical. His work was a major step towards the eventual separation of science from both philosophy and religion, a milestone in the development of human thought.

William Reville is an emeritus professor of biochemistry and public awareness of science officer at UCC;