Football Physics

Emico Okuno , Marcos Duarte

The book, written by Emico Okuno and Marcos Duarte, presents the subtleties of how a kick deforms the ball, or the reflex time needed for a goalkeeper to defend a penalty kick, beside the concepts of movement, mechanics, kinematics, force and energy.

With detailed explanations in charts, practical examples and solved exercises, the book complements the classroom studies and also provides hints, e. g., how to kick a ball with effect, proving that football is an art full of science. The work aimed at high school students has the merit of bringing Physics to everyday life, stimulating the scientific discovery.

Original title
Física do futebol
Year of publication

About the authors

Emico Okuno

Emico Okuno has a PhD in Physics from University of São Paulo (USP) and completed her post-doctorate research in University of Parma (Italy). She was a professor at the Physics Institute of USP from 1960 to 2006.

Author's CV (in portuguese).

Marcos Duarte

Marcos Duarte has a PhD in Physics from University of São Paulo (USP) and completed his post-doctorate research in University of Pennsylvania. He is a professor and a researcher in the program of Biomedical Engineering at Universidade Federal do ABC.

Click here for the author's CV.

Excerpts from the beginning of each chapter:

Chapter 1: Motion

Football is movement and the ball at rest is just a pause. The game begins when the ball starts to roll. However, the real game happens when we witness brilliant dribbling techniques, perfect kicks, phenomenal defenses, and finally the GOAL. The absolute state of rest and stillness preceding the execution of a penalty shot in the finals of a national championship are curtains hiding the celebration of the movement, whether it brings joy or sorrow.

In this chapter we will see how motion is described in detail in physics. For now, let’s not worry about how the motion was initiated or caused. This description of motion without regard to its causes is known as kinematics – as we will see.


Chapter 2: Force
Any change in the state of motion of anything in football, the subtle touch between the feet of the opponent, the failed attempt to prevent the rally, the authoritative whistle marking a penalty, the strong, well placed penalty kick, the goalkeeper`s jump in vain with the scream in unison-goal- is related to the action of a force.

Just as in football, which has its 17 rules, in mechanics there are fundamental rules called laws. Three of these laws express the quantitative relationship between motion and force. The study of the forces and their relations with motion belongs to the area of mechanics called dynamics, which we will see in this chapter.


Chapter 3: Energy

Energy is another fundamental physical concept we use very much in our day to day activities and, in particular, in football. In this chapter we will see how energy is closely related to the motion of bodies. Therefore, we discuss in detail only one of the many forms of energy: mechanical energy. Energy is quite indispensable in our lives. We know that there are various forms of energy: electrical energy that equipment in our homes consume, chemical energy of fuels for cars and the food we eat, and the energy related to the motion of bodies are examples of different forms of energy with which we have contact on a daily basis. These examples illustrate a fundamental property of energy: its capacity for transformation.


Chapter 4: Fluids

Liquids and gases are part of a class of state of matter called fluid. All that exists on earth is wrapped in air, which is a fluid.

Legend has it that one day, Didi (one of the greatest Brazilian players of all time) had a foot injure and, being unable to kick the ball normally, decided to kick it with the outside of his foot, hitting its side, and not in the center. What happened, as all footballers know, made history: the ball made an amazing curve, while revolving around itself, like never before. From the point of view of physics, what had happened was that the ball in motion and rotating around itself had given rise to another force between it and the fluid, air.


Soccer and physics are as inseparable as peanut butter and jelly. Soccer is movement, but not an ordinary movement, disorderly and lawless. Each player is the artist of something unique to be on set on a field set by boundaries (laws). Each player´s action has its own intentions, which are partly shaped by the laws (rules) of Soccer and the laws of nature. Just as it is impossible to predict the final painting on a canvas by looking at the paints in the painter´s tray, so is the outcome of a player´s action - even with all the knowledge of the laws of nature. Many say this is what makes Soccer so exciting, and that Brazilian Soccer is perhaps the closest to a creative art this sport can get. This book has no intention whatsoever to breakdown such a charm, even because it would be impossible to do so.

Understanding the physics of Soccer probably will not make anyone play better, but it will help you understand a little more about this fascinating game. And for those who want to understand the laws of motion, studying The Physics of Soccer is a more relaxed way to do it. The objective of this book is to show to Soccer fans and curious physicists the Physics behind Soccer.

This book not only teaches physics, but also the very rules of Soccer and everything related to the mechanics that happens in it. The concepts of mechanics are described in order to cover all content in the curriculum of physics studies in the first year of high school.

The Physics of Soccer describes in detail why things happen the way they do in Mechanics. There are mathematical formulas, but we always try to show the motivation that lies behind them. The way it´s been written make us believe it could even be used a self-teaching Physics book.