Galilean mechanicsAn apple falls from a tree. How does one understand the free fall phenomenon? Galileo began with the assumption that the motion proceeds according to the simplest possible law: equal increase in velocity in equal periods of time. Today we call it uniformly accelerated motion, in modern notation v∝t. Yet, the correctness of this assumption couldnot be shown by direct experiment because instantaneous velocity could not be measured. Galileo wrote down the distance traveled by a free-falling body as a function of time by applying the “mean-speed theorem” which claims that a body moving with a uniformly accelerated motion covers the same distance in a given time as if it were to move for the sameduration with a uniform speed equal to its mean speed.26Mathematically, the distance is givenby s=12vt. Hence, the distances traveled by a body in free fall are proportional to the squares of the times, s∝t2. Hence: s1t12=s2t22=s3t32=…This result can be experimentally verified since both the distance and time can be measured, and the proportionality checked thereby verifying the assumption v∝t. But free fall involves very small time intervals that were difficult to measure. Galileo overcame this difficulty by employing an inclined plane with a small angle of inclination. This could “slow 24René Descartes (1596 – 1650 CE), a French philosopher, mathematician, and scientist.25Principiais the short form of Philosophiæ Naturalis Principia Mathematica(Latin for Mathematical Principles of Natural Philosophy).26The theorem was proposed by the Merton scholars in the 14thcentury. Lindberg, D (2007), pp. 304 – 305.
GE ST: History of Science and Technology in the West P. 19 /25 down” free fall to the point where he could measure the time intervals with sufficient accuracy using the instruments available. Galileo further argued that increasing the plane’s angle of inclination was equivalent to gradually approaching the case of free fall.This is the first time in the history of mechanics that a detailed presentation of an experiment and the experimental conditions in the manner that we would expect in a scientific publication today. Galileo’s approach to science demonstrates the roles of experimental investigation in scientific theory. (a) Galileo began with an explanation of the terms; in this case, he defined what is meant by free fall with physical quantities. (b) He formulated a hypothesis concerning the expected distance-time relation. (c) From this hypothesis he then analytically (or mathematically) derived relationships that can be verified experimentally. (d) Finally, Galileo performed experiments to test the theoretical predictions. Galileo demonstrated a modern appreciation of the roles and the relationship among theory, mathematics, and experiments.