One of the most famous stories about Galileo is that he dropped balls of different masses from the Leaning Tower of Pisa to demonstrate that their velocity of descent was independent of their mass (excluding the limited effect of air resistance). This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. Though the story of the tower first appeared in a biography by Galileo's pupil Viviani, it is now not generally believed to be true. However, Galileo did do experiments involving balls rolling down inclined planes, which showed the same thing. He determined the correct mathematical law for acceleration: the total distance covered, starting from rest, is proportional to the square of the time. He concluded that falling objects are accelerated independently of their mass, and that objects retain their velocity unless a force acts upon them.

Galileo also noted that a pendulum's swings always take the same amount of time, independently of the amplitude. While Galileo believed this equality of period to be exact, it is only approximate, applying to small swings. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology.)

In the early 1600s, Galileo and an assistant tried to measure the speed of light. They stood on different hilltops, each holding a shuttered lantern. Galileo would open his shutter, and, as soon as his assistant saw the flash, he would open his shutter. At a distance of less than a mile, he could detect no delay greater than when he and the assistant were a few yards apart. While he could reach no conclusion on whether light propagated instantaneously, he recognized that the distance over which he had made the measurement was small.