Galileo and Constant Acceleration

Galileo plays a vital role in the history of astronomy, mathematics, philosophy, and physics with his discoveries of the astronomical telescope, the thermometer, the compass, the pendulum, and many more. While these discoveries paved the way to many new insights about the world around us, another important finding that is attributed to Galileo is that he taught the world about the Earth’s gravitational pull.

Galileo had determined that he could time each swing of a stone on a rope by his pulse to see if the ‘swing time’ remained the same. He was astonished to find that timing of the swings was independent from that actual size of the stone he used. He then decided that if different sizes of stone on the same length of string swung the same amount of time, that different sized objects dropped from a height would land at the same time.

While many believe that Galileo did indeed observe this by dropping two different sized objects from the Leaning Tower of Pisa, we know now that this theory is not correct. Two different sized objects will take different amounts of time to reach the same destination if dropped from the Leaning Tower of Pisa. Instead, we theorize that Galileo may have “thought” this experiment, rather than actually observe it.

Because of this belief, Galileo decided to prove his theory mathematically. While he could not properly observe an object in free fall to time it, he decided to slow down the ‘free fall.’ He experimented using an inclined plane and had balls travel down the plane.

To measure the time of the traveling balls, he used a water clock. The amount of water that poured out of the spigot during an ‘interval’ represented the amount of time. He found that no matter what the size of the ball, the speed of the ball and the distance it traveled remained the same. He could then determine that this constant acceleration was due to gravity.

Before Galileo’s experiments regarding vertical motion, many believed the Aristotelian idea that an object will naturally come to a stop unless something (a force) acts upon it. Galileo believed that an object will retain its velocity unless something (a force) were to act upon it.

While this belief had been stated by others in the past, Galileo was the first to experiment and mathematically prove the “law of inertia.” While his idea eventually became Newton’s First Law, it was originally stated as: “A body moving on a level surface will continue in the same direction at constant speed unless disturbed.”