# Air Resistance: Definition, Formula & Examples

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• 0:01 Definition of Air Resistance
• 1:23 Air Resistance in Mathematics
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Lesson Transcript
Instructor: Sergey Segal

Sergey has a Masters in Biomedical Engineering and has taught science and mathematics courses at the University of Wisconsin-Madison.

Air resistance is an important phenomenon in physics and other scientific fields. In this lesson, we'll learn what happens when air molecules exert force on solid objects, and then test your new knowledge with a short quiz.

## Definition of Air Resistance

Imagine dropping an apple from the top of a skyscraper and watching it fall. Intuitively, you might guess that it will be falling at a faster speed right before hitting the ground than at the moment you released it. In other words, the apple sped up while falling. However, is there a way to quantitatively describe an object's motion through air? If we were to drop the same apple from an airplane, would it ever reach a maximum downward velocity?

Air resistance is the force that air exerts on objects moving through it. Scientists often refer to this force as drag or drag force, a term we'll use interchangeably throughout the lesson. Note that in many cases, 'drag' can refer to any type of fluid, not just air. However, for the purposes of our discussion, we'll always refer to air as the fluid.

Typically, this force is directed opposite to the object's motion, thereby slowing it down. If you've ever held your hand out of a speeding car's window, you've noticed how the air pushes your hand in a direction opposite to that of the car's movement. When a piece of paper is dropped to the ground, air resistance slows down its fall.

Although we'll only be focusing on the force that air molecules exert on solid objects, it's important to mention that this force may exist between different fluid layers in addition to existing between a solid object and a fluid. Now, let's discuss air resistance from a mathematical perspective.

## Air Resistance in Mathematics

The air resistance force is dependent on several factors, as shown in this equation:

Note that if the velocity of the object doubles, the drag force is quadrupled. You should also keep in mind that the drag coefficient is a dimensionless number, derived from lab testing, that varies for different types of fluids and objects.

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