A biography by Galileo's pupil Vincenzo
Viviani stated that Galileo had dropped balls
of the same material, but different masses ,
from the Leaning Tower of Pisa to
demonstrate that their time of descent was
independent of their mass.[126] This was
contrary to what Aristotle had taught: that
heavy objects fall faster than lighter ones, in
direct proportion to weight. [127] While this
story has been retold in popular accounts,
there is no account by Galileo himself of such
an experiment, and it is generally accepted
by historians that it was at most a thought
experiment which did not actually take place.
[128] An exception is Drake, [129] who argues
that the experiment did take place, more or
less as Viviani described it. The experiment
described was actually performed by Simon
Stevin (commonly known as Stevinus), [23]
although the building used was actually the
church tower in Delft in 1586. [130] However
most of his experiments with falling bodies
were carried out using inclined planes where
both the issues of timing and wind resistance
were much reduced.
In his 1638 Discorsi , Galileo's character
Salviati, widely regarded as Galileo's
spokesman, held that all unequal weights
would fall with the same finite speed in a
vacuum. But this had previously been
proposed by Lucretius[131] and Simon Stevin.
[132] Cristiano Banti 's Salviati also held it
could be experimentally demonstrated by the
comparison of pendulum motions in air with
bobs of lead and of cork which had different
weight but which were otherwise similar.
Galileo proposed that a falling body would fall
with a uniform acceleration, as long as the
resistance of the medium through which it
was falling remained negligible, or in the
limiting case of its falling through a vacuum.
[133] He also derived the correct kinematical
law for the distance travelled during a uniform
acceleration starting from rest—namely, that it
is proportional to the square of the elapsed
time ( d ∝ t 2 ). [134] Prior to Galileo, Nicole
Oresme , in the 14th century, had derived the
times-squared law for uniformly accelerated
change, [135] and Domingo de Soto had
suggested in the 16th century that bodies
falling through a homogeneous medium would
be uniformly accelerated. [136] Galileo
expressed the time-squared 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).
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 John Philoponus
centuries earlier, as had Jean Buridan , and
according to Joseph Needham , Mo Tzu had
proposed it centuries before either of them;
nevertheless, Galileo was the first to express
it mathematically, verify it experimentally, and
introduce the idea of frictional force , the key
breakthrough in validating the concept.
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).
Dome of the Cathedral of Pisa with
the "lamp of Galileo"
See also: Equations for a falling body
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