Message #74566

[Bianca]

Galileo arrived at the correct mathematical law for uniform acceleration: the total distance covered, starting from rest, is proportional to the square of the time (), already discovered by Domingo de Soto in the 16th century. He expressed this law using geometrical constructions and mathematically-precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms).

But he erroneously claimed gravitational free-fall universally is uniformly accelerated as thefundamental law of motion of his cosmology and cosmogony, a claim that was never generally accepted and soon refuted by the 1660s discovery that it is exponentially increasingly accelerated (a difform motion in scholastic terms) and inversely proportional to distance from its gravitational centre.

He also concluded that objects retain their velocity unless a force—often friction—acts upon them, refuting the generally accepted Aristotelian hypothesis that objects "naturally" slow down and stop unless a force acts upon them (philosophical ideas relating to inertia had been proposed by Ibn al-Haytham centuries earlier, as had Jean Buridan, and according to Joseph Needham, Mo Tzu had proposed it centuries before either of them, but this was the first time that it had been mathematically expressed, verified experimentally, and introduced the idea of frictional force, the key breakthrough in validating inertia). Galileo's Principle of Inertia stated:


"A body moving on a level surface will continue in the same direction at constant speed unless disturbed."


This principle was incorporated into Newton's laws of motion (first law).

 
Galileo also noted that a pendulum's swings always take the same amount of time, independently of
the amplitude. The story goes that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. While Galileo believed this equality of period to be exact, it is only an approximation appropriate to small amplitudes. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology above)