Resource: Galileo's Inclined Plane

Galileo thought a great deal about the motion of falling objects. Specifically, he was interested in the forces that acted upon objects in free-fall and whether those forces affect different types of objects differently.

In Galileo's time, Aristotle's centuries-old assertion that heavier objects fall faster than lighter objects was almost universally accepted. Even today, most people would predict that a feather will drift to the ground more slowly than a hammer, but they might not be able to explain why. Galileo acknowledged this difference in falling time, but wondered if it was due to the mass of the objects and gravity's pull on that mass, or to some other force that was being overlooked. For years, he conducted real-world experiments and "thought experiments" to test his ideas.

Most falling objects move quickly. Even with a modern stopwatch, it is difficult to accurately measure an object's free-fall velocity or its rate of acceleration. Having no such timepiece, Galileo might have considered a study of falling objects impossible.

However, Galileo was nothing if not ingenious. He had the idea that a ball rolling down an incline would accelerate in the same way as a free-falling object, but more slowly. Using a straight, gently sloped piece of wood with a groove running down the center -- an inclined plane -- he was able to "dilute" gravity's effect. The inclined plane thus allowed Galileo to accurately measure acceleration with simple instruments and ultimately to prove that, in the absence of other forces such as air resistance, gravity causes all falling objects to accelerate toward Earth at the same rate.

How did Galileo slow down motion so he could measure the motion of a falling object?

Make a chart that shows the pattern Galileo discovered when he measured the units of distance a falling object covers in each unit of time.

Use a sketch to explain what "this beautiful numerical progression--one, three, five, seven" means. What is special about the sums of odd integers?

Why do the 50 stars on the American flag fit so well? Try adding up the rows of stars, starting in a corner. Notice the sequence 1+3+5+ and so on. Why does it stop at 9?