# The Rolling Ball Experiments: Galileo’s Terrestrial Mechanics

FROM THE LECTURE SERIES: THE JOY OF SCIENCE

## To many scientists, Galileo Galilei was honored first and foremost as the founder of experimental science. Along with many of his predecessors and contemporaries, he sought to understand the mathematical forms and the laws that described falling objects. But, why was this important, and how did Galileo resolve the questions?

### Disproving Aristotle’s Ideas about Falling Objects

In an age when cannons had just been developed (and gunpowder and explosives), people needed to be able to fire objects accurately from one place to another. They needed to know how objects moved on Earth. They needed to know what sort of curving paths objects adopted when they were fired in the Earth’s gravity. Aristotle had said that heavier objects fall faster than light objects, and this is a claim that Galileo demonstrated to be quite false.

The story that Galileo dropped two balls from the Leaning Tower of Pisa is probably apocryphal, but he did do a similar experiment. He took two objects of different masses and different sizes and dropped them from a high place, and found that they landed at exactly the same time. So, through an empirical experimental approach, he showed that the reasoning, the rationale, of Aristotle was wrong.

This is a transcript from the video series The Joy of Science. Watch it now, on Wondrium.

### Galileo’s Rolling Ball Experiment

Realizing that free-falling objects move too fast to measure with any sort of conventional techniques of the day—the watches and clocks that were available at that point—Galileo devised an ingenious, adjustable ramp to dilute the effects of gravity.

What he would do was measure a distance along the inclined plane, and then time the fall. This is called the rolling ball experiment.

### Accurate Time Measurement

But the main problem with the ‘rolling ball’ experiment is that accurate time measurements are needed. In Galileo’s day, there weren’t really any accurate timepieces. At first, Galileo used his pulse, but that wasn’t very accurate. Then he invented an ingenious way to measure time.

He said,

We employed a large vessel of water and placed it in an elevated position. To the bottom of this vessel was soldered a pipe of small diameter, giving a thin jet of water. We collected this water in a small glass during the time of each descent. The water thus collected was weighed after each descent on a very accurate balance. The differences and ratios of these weights gave us the differences and ratios of the times.

Now that he had the means to measure time, Galileo and his assistants conducted numerous repetitions—another aspect of experimental science.

In such experiments repeated a full 100 times we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the channel along which we rolled the ball.

### The Conclusions of the Rolling Ball Experiment

If, for example, it took an object six units of time to go an entire length, then a guess might be that it would only take three units to go half as far as the marked length.

But Galileo found that it takes four units to travel half the distance; three units to travel one-quarter of the distance, and six units to travel the entire distance.

So, the distance traveled is proportional to the square of time. That was Galileo’s great discovery with the rolling ball experiment.

A fascinating aspect of this experiment is that Galileo did not conduct the rolling ball experiment to discover a mathematical relationship between time and distance. Rather, he used the apparatus to confirm his conviction that velocity and time bear the simplest kind of relationship to each other.

That is, the velocity of a falling object is proportional to the time of its fall. He called this steadily increasing velocity, uniform acceleration. Galileo also demonstrated mathematically that this result was equivalent to saying that the distance traveled by a falling object is equal to the square of the time of its fall.

### Other Experiments in Terrestrial Mechanics

Galileo devised lots of other experiments in his study of terrestrial mechanics. One of his most famous is his study of pendulums where he found that longer pendulums swing more slowly than shorter ones and the rate of speed is independent of the mass of the pendulum.

Galileo also discovered a key principle regarding ballistics, that is, the way objects fly through the air. He found that the horizontal motion of a falling object is completely independent of the vertical fall. For example, he cited the example of a heavy object dropped from the mast of a moving ship.

Aristotelian philosophers held that an object would land some distance behind the mast of the moving ship—if it was dropped from high up the object would fall backward, and the ship would move out from under it. But Galileo said no, the object is moving along with the ship and is going to fall right at the base of the mast.

He tested a lot of other ideas experimentally. For example, he fired cannonballs horizontally off a cliff and observed the curving path of the fall. And what he found is that when you do that, you always find the same type of curved path, called a parabola. He found that all falling objects will follow the same kind of path.

So, Galileo ought to be remembered not just as a great astronomer, but also as the scientist who first discovered the basic rules of terrestrial mechanics: the rules of how objects moved on the Earth.

### Common Questions about Galileo’s Rolling Ball Experiments

Q. Why did Galileo devise a ramp for his experiments on falling objects?

Realizing that free-falling objects move too fast to measure with any sort of conventional techniques of his age, Galileo devised an ingenious, adjustable ramp to dilute the effects of gravity and slow objects down to observable speeds.

Q. What was the time-related problem Galileo had to solve before he could undertake the rolling ball experiment?

The main problem with the rolling ball experiment was that Galileo needed accurate time measurements. He invented an ingenious way to measure time, which involved weighing the water expelled from a pipe in the time the ball rolled down the incline.

Q. What was the conclusion of Galileo’s rolling ball experiments?

The conclusion of the rolling ball experiments was that the velocity of a falling object is proportional to the time of its fall. Galileo proved that this means that the distance traveled by the ball was proportional to the square of time.