Free-fall acceleration: Rate of acceleration due to the force of Earth's gravity.

Galileo Galilei is reputed to have conducted an interesting experiment several hundred years ago. According to legend, he dropped two balls with different masses off the Leaning Tower of Pisa and found that both landed at the same time. Their differing masses did not change the time it took them to fall. (We say he was “reputed to have” because there is little evidence that he in fact conducted this experiment. He was more of a “roll balls down a plane” experimenter.)

Today this experiment is used to demonstrate that free-fall acceleration is constant: that the acceleration of a falling object due solely to the force of gravity is constant, regardless of the object’s mass or density. The two balls landed at the same time because they started with the same initial velocity, traveled the same distance and accelerated at the same rate. In 1971, the commander of Apollo 15 conducted a version of the experiment on the Moon, and demonstrated that in the absence of air resistance, a hammer and a feather accelerated at the same rate and reached the surface at the same moment.

In Concept 1, you see a photograph that illustrates free-fall acceleration. Pictures of a freely falling egg were taken every 2/15 of a second. Since the egg’s speed constantly increases, the distance between the images increases over time. Greater displacement over the same interval of time means its velocity is increasing in magnitude; it is accelerating.

Free-fall acceleration is the acceleration caused by the force of the Earth’s gravity, ignoring other factors like air resistance. It is sometimes stated as the rate of acceleration in a vacuum, where there is no air resistance. Near the Earth’s surface, its magnitude is 9.80 meters per second squared. The letter g represents this value. The value of g varies slightly based on location. It is less at the Earth's poles than at the equator, and is also less atop a tall mountain than at sea level.

The acceleration of 9.80 m/s² occurs in a vacuum. In the Earth’s atmosphere, a feather and a small lead ball dropped from the same height will not land at the same time because the feather, with its greater surface area, experiences more air resistance. Since it has less mass than the ball, gravity exerts less force on it to overcome the larger air resistance. The acceleration will also be different with two objects of the same mass but different surface areas: A flat sheet of paper will take longer to reach the ground than the same sheet crumpled up into a ball.

By convention, “up” is positive, and “down” is negative, like the values on the y axis of a graph. This means when using g in problems, we state free-fall acceleration as negative 9.80 m/s². To make this distinction, we typically use a or a_y when we are using the negative sign to indicate the direction of free-fall acceleration.

Free-fall acceleration occurs regardless of the direction in which an object is moving. For example, if you throw a ball straight up in the air, it will slow down, accelerating at −9.80 m/s² until it reaches zero velocity. At that point, it will then begin to fall back toward the ground and continue to accelerate toward the ground at the same rate. This means its velocity will become increasingly negative as it moves back toward the ground.

The two example problems in this section stress these points. For instance, Example 2 on the right asks you to calculate how long it will take a ball thrown up into the air to reach its zero velocity point (the peak of its motion) and its acceleration at that point.