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The Physics of Sports: How Science Helps Athletes Break Records and Push Boundaries

Krystal DeVille

Updated on: March 31, 2024

In the world of sports, athletes constantly push the boundaries of what’s possible, break records, and achieve feats that were once thought impossible. But behind these incredible performances, a hidden player often goes unnoticed: physics. Understanding the principles of physics can provide a deeper insight into how athletes achieve their remarkable feats and how they can push their limits even further.

Table of Contents

The Science of Speed

One of the most critical aspects of many sports is speed. Whether it’s a sprinter racing on the track or a swimmer cutting through the water, understanding the physics of motion can help athletes move faster. By studying factors like air resistance, friction, and the biomechanics of movement, athletes can refine their techniques to maximize their speed.

The Power of Momentum

In sports like football and rugby, momentum plays a crucial role. The momentum of an athlete or an object (like a ball) depends on its mass and velocity. Understanding how to maximize momentum can give athletes an edge in these sports.

The Art of Aerodynamics

For sports involving high speeds or flight—like cycling, skiing, or long jump—understanding aerodynamics is key. The shape and surface of an object can significantly affect the air resistance it encounters. That’s why cyclists wear streamlined helmets and skiers adopt specific postures to minimize air resistance and maximize their speed.

The Magic of Spin

In sports like tennis, table tennis, or golf, putting spin on a ball can drastically alter its trajectory. This is due to the Magnus effect, a phenomenon in physics where a spinning object moving through a fluid (like air) experiences a force perpendicular to its path.

The Secret of Leverage

In sports like baseball or golf, the principle of leverage is crucial for maximizing the distance a ball travels. By hitting the ball at the end of the bat or club—farthest from the point of rotation—players can achieve the highest speeds and longest distances.

The Mystery of the Sweet Spot

In many sports, hitting an object at its “sweet spot”—the point where the impact feels best and produces the best result—can make a significant difference. The sweet spot is a complex interplay of physics principles, including vibrations, shock waves, and the transfer of momentum.

The Wonder of Fluid Dynamics

In swimming and other water sports, understanding fluid dynamics—the study of how fluids move—can be a game-changer. Swimmers can optimize their strokes and body positions to move more efficiently through the water, reducing drag and conserving energy.

The Intricacies of Angular Momentum

Gymnasts, figure skaters, and divers all rely on the conservation of angular momentum to perform their impressive flips and spins. By changing their body shape—extending their limbs out to slow down or pulling them in to speed up—they can control their rotation speed.

The Power of Elastic Energy

In sports like pole vaulting or long jump, athletes convert their kinetic energy (energy of motion) into elastic potential energy to achieve their incredible feats. The more efficiently they can make this energy conversion, the better their performance.

The Impact of Gravity

Last but not least, gravity plays a crucial role in virtually every sport. Whether it’s keeping a soccer ball on its downward trajectory or pulling a diver toward the water, understanding the effects of gravity can help athletes predict and control their movements.

In conclusion, the world of sports is a playground for physics. By understanding and applying these principles, athletes can push their boundaries, break records, and take their performance to the next level.

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Photo: Golf: You learn to play a game like this by hitting a ball hundreds or thousands of times. Your brain learns to correlate the way you move your muscles with the places where the ball ends up; eventually, after enough practice, you can place the ball wherever you want. In theory, a robot could play just as effectively if you programmed it with the laws of physics, or if you let it practice and learn from its mistakes using a neural network (a type of computer model that learns from experience like a brain). Photo by Eric Tretter courtesy of US Navy and Wikimedia Commons .

Photo: Scoring a goal: sheer skill or cunning physics? Your brain calculates the trajectory of the ball and figures out how to kick it to reach a particular spot. If there are people in the way, you might spin the ball so it curves through the air and bends around them. Skillful players learn how to do this by trial and error, but a scientist could also figure out how to achieve the same effect using the laws of aerodynamics. Photo by Gary Nichols courtesy of US Navy .

Photo: When two billiard balls collide, we can get almost total energy transfer—known as an elastic collision. Photo by Brittany Y. Bateman courtesy of US Air Force .

Photo: Baseball involves a hard wooden or metal bat and a fairly hard ball made of leather and rubber. However, because there is some "give" in the ball, the collision between the bat and the ball is less elastic than in billiards. Photo by Shannon McMillan courtesy of US Marine Corps .

Photo: Kicking or heading a soccer ball involves an inelastic collision with your body. Photo by Kristopher Radder courtesy of US Navy and Wikimedia Commons .

Animation: A soft ball deforms as it hits a hard surface. The materials the ball is made from squash and compress, and the air inside is also compressed, exerting a pressure that makes the ball quickly return to shape. Although this process looks completely reversible, some energy is always lost, which is why a bouncing ball can never return to exactly the same height from which it originally fell.

Chart: Which sports balls have most energy? We can figure out the kinetic energy of a ball with the formula ½mv 2 . Plugging in the masses and (higher-end) speeds, we get these sorts of estimates. I would have guessed that golf balls had most energy because they seem to be going so fast, but they're also very light. Soccer balls, kicked hard, have surprisingly high energy because they go faster than you think and weigh almost 10 times more than golf balls. Which balls hurt most when they hit you? Generally, harder and smaller balls (golf balls) because they dissipate their energy very quickly over a small area, which means they exert more force and pressure on your body. That's also the idea behind bullets, except they're pointed to move faster and help penetrate your body. Interestingly, if you check out the similar chart I drew in my bullets article, you'll find modest handgun bullets have comparable energy to fast-moving sports balls (hundreds of joules).

How do bats work?

Photo: Why is table tennis so fast and furious? Consider the science. The bat, ball, and playing surface are all hard, so the collisions are elastic and fast. The ball is small and light, so it accelerates quickly. The table is very small, so the fast-moving ball travels very quickly from one end to the other. Imagine if the ball was bigger and softer, the table was made of very soft rubber, and the bat was more like a tennis racket. That would make the game much slower and far less interesting. Photo by Anton Wendler courtesy of US Navy and DVIDS .

Photo: When you bowl, your brain instantly works out how to control your muscles to throw the ball to reach a precise position in space. On paper, that's simple physics, but it's amazing that our brains and bodies can do things like this instinctively, with no calculations at all. Photo by Jon Dasbach courtesy of US Navy and Wikimedia Commons .

Photo: Long jump is all about conservation of energy and momentum. Once you're airborne, there's no way to get any more energy, so the run-up is crucial: the more kinetic energy you give you body the further you'll go. In midair, you can move your legs further forward by bringing your arms around and back, as this jumper is just about to do. There's a wonderful photo of the sequence of movements a long jumper goes through in Anatomy of an Athlete , The Sydney Morning Herald, 2016. Photo by Matthew A. Ebarb courtesy of US Navy and Wikimedia Commons .

Artwork: Pole vault is a good example of the conservation of energy. 1) During the run-up, your body tries to gain as much kinetic energy as possible. This is vital because, once you're airborne, there's no way to gain extra energy. 2) When you stick the pole into the ground, it bends and converts your kinetic energy into elastic potential energy. 3) As the pole straightens, it gives the kinetic energy back to your body. The pole's job is to help you convert kinetic energy (your running energy) into potential energy (the energy you have when you climb into the air) and horizontal motion into vertical motion. 4) When you let go of the pole, you're climbing upward, working against the force of gravity. Your body's kinetic energy is gradually converted to potential energy as you climb, which is why you start to slow down. 5) At your highest point, as you cross the bar, your body has maximum potential energy. All the energy you have at this point came from the kinetic energy of your original run-up.

Photo: Here's the actual sequence of moves in the pole vault. These are photos of Cale Simmons competing in the men's pole vault finals at the US Olympic Team Track and Field Trials in 2016. Photos by Tom "Drac" Williams courtesy of US Air Force and DVIDS .

Photo: Aerodynamics is as important to cyclists as it is to designers of race cars and jet planes, which is why they wear tight clothes and lean forward like this. Although you can't see it in this photo, racing cyclists also use special handlebars that position their elbows much closer to their torsos, significantly reducing drag.

Photo: Skateboarders master physics instinctively: skating is all about center-of-gravity, Newton's laws, conservation of energy, and conservation of angular momentum. In this trick, widely spread arms give better balance by increasing the skater's moment of inertia. Photo by Natasha Stannard courtesy of US Air Force and DVIDS .

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The physics of sports

July 25, 2016 | 10 min read

By Carina Arasa Cid, PhD

From swimming to sports gear, physics principles are at the heart of athletics

Update:  The articles in this story are now freely available until October 31, 2016. Starting August 5, the Olympics in Rio will gather more than 10,000 athletes from 206 countries competing in 42 disciplines. Most of the athletes have put in years of intense, focused physical and psychological training.

For those who will be watching them, or who play sports themselves, we have created a virtual special issue called  The Physics of Sports . The articles here are freely available until October 31, 2016.

Understanding the physics of motion can affect all areas of sports, from helping athletes move faster, to preventing injuries, planning more efficient trainings, and developing aerodynamic equipment and clothing.

Physics and sports are intimately connected. This is because every sport’s discipline depends on the ability of an athlete to exercise a force, and a force is one of the key elements of  Newton’s laws of motion opens in new tab/window  and other elementary physics concepts.

Work and energy in pole vaulting

Work and energy are among the most important concepts of physics. Both, work and energy, play an important role in sports.

In physics, work is defined as the result of a force moving an object a certain distance. Thus, force and work are directly proportional to each other. In addition, the concepts of work and energy are closely related. Hence, work transfers energy from one place to another or one form to another.

During a pole vaulting performed by athletes, different types of energy are involved. First, the athletes transform chemical energy into kinetic energy of their body while running. Part of this kinetic energy becomes elastic potential energy, as observed by the deformation of the pole; the rest of energy becomes gravitational potential energy, which again it is transformed into kinetic energy while the athletes fall away from the bar.

In the following articles, the authors explore these principals in pole vaulting:

Schade, F., Arampatzis, A.: “ Influence of pole plant time on the performance of a special jump and plant exercise in the pole vault opens in new tab/window ,” Journal of Biomechanics (June 2012)

Dillman, C.J., Nelson, R.C.: “The mechanical energy transformations of pole vaulting with a fiberglass pole,"  Journal of Biomechanics (August 1968)

Angular momentum in skating

In physics, if a system is isolated from its surroundings, that is, if no external forces acting on it, there are three  conserved  quantities (which means they maintain the same level or energy or transform into other types of energy): energy, linear momentum and angular momentum. In classical mechanics, conservation of linear momentum (the product of the mass and velocity of an object) is implied by Newton's laws.

Angular momentum – also known as rotational momentum – is the quantity of rotational motion a body has. It is the product of the moment of inertia (i.e., the product of the mass of the object and the square of its perpendicular distance from the axis of rotation) and rotational velocity.

Conservation of angular momentum is another important concept. For example, consider a figure skater who turns on the tip of her skates. In the absence of external forces, the angular momentum is almost constant. When a figure skater draws her arms and a leg inward, she reduces the distance between the axis of rotation and some of her mass, therefore reducing the moment of inertia and her friction with the air. Since angular momentum is conserved, her rotational velocity must increase to compensate.

Friction in skating and swimming

The force of friction is the force resisting the displacement of one surface over another and material elements sliding against each other. In all sports, friction represents a braking force that needs to be overcome; the more you can overcome this force, the better your chances of success. Using the example of skating, Dr. Martine Le Berre a researcher at  L’Institut des Sciences Moléculaires d’Orsay (ISMO) opens in new tab/window  in France, explained: "Skating is possible because the melted liquid layer in-between ice and skate has macroscopic thickness. It is due to the heat generated by friction. The thickness of the melted layer is deduced from the basic equations of fluid mechanics and Stefan law, it depends on the velocity and mass of the skater and the radius of profile and bite angle of the blade. We show that such a lubricating melted water layer always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect)."

Prof. Yves Pomeau, PhD, and Martine Le Berre, PhD

During the last 10 years, Dr. Le Berre has collaborated with Prof. Yves Pomeau of the University of Arizona on topics ranging from the quantum tunnel effect in fibers, to earthquake predictions, supernovae description, ice-skating, the study of irreversible phenoma like turbulent flows, and recently the fluorescent emission of a single atom. Recently they published an article on ice-skating:

Le Berre, M., Pomeau, Y.: “ Theory of ice-skating opens in new tab/window ” International Journal of Non-Linear Mechanics (June 2015)

de Koning, J.J., de Groot, G., van Ingen Schenau, G.J: “ Ice friction during speed skating opens in new tab/window ” Journal of Biomechanics (June 1992)

Swimmers suffer the gravity and the force of water in swimming. Achieve efficient movement through such dense as water environment is one of the biggest challenges they have in common coaches and swimmers. Those who can move through the water while minimizing the effects of physical forces on their bodies are guaranteed to get excellent results. Swimmers must find ways of how to improve their position or arrow streamline and simultaneously reduce the area occupied by their body as it moves through the water. By reducing the area, they reduce resistance, which acts as opposing force in the water — very similar to the friction out of the water. This is because the position of the swimmer’s body is so important, and especially how they move their arms, and place the fingers in their hands.

In this article, the authors use physics to address swimming technique:

Minetti, A.E, Machtsiras, G., Masters, J.C.: “ The optimum finger spacing in human swimming opens in new tab/window ,” Journal of Biomechanics  (September 2009 )

Aerodynamics in sports equipment, football and cycling

Aerodynamics is a term of physics that describes the ability of an object to overcome air resistance. Thus, it can be applied to cycling, the bicycle composition and design, the clothing worn by the cyclist, and even the positioning of the rider on the bicycle.

Dr.  Samir Aouadi opens in new tab/window , Editor of  Surface and Coatings Technology opens in new tab/window  and Professor of Materials Science and Engineering at the University of North Texas, has over 15 years of experience in using various techniques to modify materials’ surfaces. He explained:

Samir Aouadi, PhD

"Coatings are currently used to extend the lifetime and enhance the performance of several components that are used by athletes. For example, coatings are used to reduce friction improve on the wear resistance of bearings used in high performance bicycle bearings. In addition, protective ceramic coatings are also used for golf club heads, air rifle barrels, and in various bow modules used in archery to provide surface lubrication as well as impact, scratch, and corrosion/chemical protection. Finally, epoxy coatings are used on kayaks and on paddles to enhance their scratch and corrosion protection." In this related article, the authors talk about this type of materials in sports equipment:

Yu, S.S., Zhang, S., Xia, Z.W., Liu, S., Lu, H.J., Zeng, X.T. : “ Textured hybrid nanocomposite coatings for surface wear protection of sports equipment opens in new tab/window ,” Surface and Coatings Technology (February 2016)

In addition, aerodynamics plays a big role in all ball sports related. The air flow around a ball thrown through the air differs greatly depending on whether it has a smooth surface or a rough surface.

Dupeux, G., Cohen, C., Le Goff, A., Quéré, D., Clanet, C.: “

Football curves opens in new tab/window ,” Journal of Fluids and Structures (July 2011)

Hugh Trenchard, an independent researcher in Victoria, British Columbia, Canada, whose interest in peloton dynamics and collective behavior stems from his experiences as a competitive cyclist, runner and duathlete. His primary research objective is to show how self-organized principles of peloton dynamics are ubiquitous across biological collectives and represent fundamental principles of evolution. He explained: "During the Tour of France, spectators might wonder why cyclists spend most of the race in pelotons. Cyclists can travel significantly faster by traveling in pelotons and by drafting (i.e., cycling closely behind another in a zone of reduced air pressure). The shorter is the distance between cyclists, the larger is the decrease in wind resistance. Also, cyclists save more energy if they are among a group of eight cyclists than if they are drafting behind just one or two other cyclists. Therefore, aerodynamics plays an important role in cycling races."

When cyclists save energy by drafting, they also couple their energy expenditures. This means that each cyclist’s output is directly affected by the outputs of their nearest neighbors. This interactivity produces self-organized collective behavior. ‘Self-organized’ means that behavior emerges bottom-up from basic physical principles; i.e. the collective behavior is not driven by top-down demands, such as when a leader shouts at team-mates to move to certain positions. Of course top-down behavior does occur in pelotons, and cyclists constantly adjust positions according to team tactics and strategies. However, certain collective behaviors can be shown to emerge from underlying physical coupling principles. The study of collective behavior is an area of physics known as complexity theory, and includes the study of flocks, schools, and herds. Coupling among cyclists is a function of three basic physical/physiological factors: the speed or power-output of a leading cyclist, the energy saved by drafting, and the maximal sustainable outputs of the drafting rider. With these three factors, we can model the collective behavior of pelotons. We can show that there are different thresholds and phases of collective behavior. A phase transition means there is both a quantitative and qualitative difference in the pattern formation and structure of the peloton. Such phases include cyclists forming a single-file line, when they are cycling near their sustainable maximums and cannot easily pass others; and a dense and compact formation, when riders cycle at lower outputs and can pass their neighbors.

Thus, drafting is used to reduce wind resistance and it is seen in cycling, running, swimming, and car racing as well. Drafting and physiological factors produce collective behavior and phase transitions. Computational Fluid Dynamics is a computational technique used to model drafting that can help athletes to prepare and train more efficiently.

In these articles, the authors explore the principle of aerodynamics in cycling:

Trenchard, H., Ratamero, E., Richardson, A., Perc M.: “

A deceleration model of bicycle peloton dynamics and group sorting opens in new tab/window ,” Applied Mathematics and Computation  (January 2015)

Trenchard, H., Richardson, A., Ratamero, E., Perc, M.: ”

Collective behavior and the identification of phases in bicycle pelotons opens in new tab/window ”, Physica A (July 2014)

Crouch, T.N., Burton, D., Thompson, M.C., Brown, N.A.T., Sheridan, J.: ” Dynamic leg-motion and its effect on the aerodynamic performance of cyclists opens in new tab/window “, Journal of Fluids and Structures (August 2016)

Using applied mathematics for health and medicine

In these articles, the authors apply principles of applied mathematics used in medical settings to measure biological signals, detect fatigue and achieve more healthy trainings.

Sviridova, N., Sakai, K.: “ Human photoplethysmogram: New insight into chaotic characteristics opens in new tab/window ", Chaos, Solitons and Fractals (August 2015)

Billat, V.L., Mille-Hamard, L., Meyer, Y., Wesfreid, E.: “ Detection of changes in the fractal scaling of heart rate and speed in a marathon race opens in new tab/window ,” Physica A: Statistical Mechanics and its Applications (September 2009)

Fister, I., Jr., Ljubič, K , Suganthan, P.N., Perc, M., Fister, I.: “ Computational intelligence in sports: Challenges and opportunities within a new research domain opens in new tab/window ”, Applied Mathematics and Computation (July 2015)

Hugh Trenchard

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Carina arasa cid, phd.

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The Physics of Sports: Exploring the Science Behind Athletic Performances

• July 9, 2023

Sports have always been a fascinating spectacle, captivating audiences with the awe-inspiring performances of athletes. Behind every spectacular move and record-breaking achievement lies the intricate world of physics. The laws of physics govern the motions, forces, and energy exchanges that propel athletes to new heights of performance. In this blog, we’ll delve into the physics of sports and uncover the scientific principles that make seemingly impossible feats possible.

1. Projectile Motion in Athletics:

From a basketball player sinking a three-point shot to a javelin thrower launching the spear through the air, projectile motion plays a vital role in many sports. The concept of projectile motion involves the motion of objects under the influence of gravity. Understanding the optimal launch angle and velocity can significantly impact an athlete’s performance. For instance, a ski jumper must find the perfect balance between vertical and horizontal velocity to achieve maximum distance and style.

2. The Secrets of Speed:

Sprinting athletes, cyclists, and swimmers rely on Newton’s laws of motion to achieve impressive speeds. Newton’s second law, which states that force is proportional to mass times acceleration (F = ma), comes into play. Reducing air resistance and friction are crucial in achieving top speeds. Cyclists, for instance, adopt aerodynamic postures and wear specialised gear to minimise air drag.

3. The Art of Rotation:

Gymnasts, divers, and figure skaters are masters of rotational motion. Angular momentum is at the heart of their art. When a figure skater pulls their arms closer during a spin, they decrease their moment of inertia, causing an increase in rotational speed due to the conservation of angular momentum. This principle is beautifully demonstrated in the execution of a flawless triple axel.

4. Conservation of Energy:

In sports, efficiency is everything. Athletes aim to conserve and transfer energy effectively to achieve optimal results. Take, for instance, a basketball player converting the potential energy stored in their body into kinetic energy during a slam dunk. Understanding energy transformation allows athletes to fine-tune their movements and conserve valuable energy during prolonged activities.

5. Tackling Torque:

Many sports involve rotational forces known as torque. Baseball pitchers, for example, generate torque when they throw a curveball. The grip and arm motion produce an angular acceleration on the ball, leading to a curved trajectory. By understanding the principles of torque, athletes can perfect their techniques and deliver powerful performances.

6. Fluid Dynamics and Swimming:

Swimming is an exceptional showcase of fluid dynamics in action. Athletes use principles like Bernoulli’s principle, which relates the pressure of a fluid to its speed, to improve their strokes and streamline their bodies. Reduced drag is essential for competitive swimmers to gain the edge in races and break records.

7. Impact and Collisions:

Collisions are inevitable in contact sports like football and rugby. The physics of impact can be crucial for athlete safety and performance. Engineers design helmets and protective gear to absorb and distribute impact forces, reducing the risk of injury. Understanding the impulse-momentum theorem helps athletes control their movements during collisions, preventing unnecessary harm.

Conclusion:

The interplay of physics and sports is a captivating realm where science merges with human athleticism. Athletes, coaches, and sports scientists continue to explore these principles to push the boundaries of human performance. From the graceful motions of figure skaters to the explosive power of sprinters, each sport embodies a unique blend of physics and skill.

The next time you witness a jaw-dropping sports moment, take a moment to appreciate the scientific marvels that make it possible. The physics of sports not only enriches our understanding of athletic achievements but also reminds us of the boundless potential of human capability.

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The European Physical Society (EPS) is a not for profit association whose members include 41 National Physical Societies in Europe, individuals from all fields of physics, and European research institutions.

As a learned society, the EPS engages in activities that strengthen ties among the physicists in Europe. As a federation of National Physical Societies, the EPS studies issues of concern to all European countries relating to physics research, science policy and education.

Focus on Physics of Sport

Guest editors.

Simon Choppin Sheffield Hallam University, UK Angela Fösel FAU Erlangen-Nuremberg, Germany

10 June 2016 marks the beginning of the European Football Championship in France, and only four weeks later, the Olympic Summer Games are due to start! This makes 2016 a highlights for sports enthusiasts all over the world. Millions of fans shall watch the football matches and the Olympic Games live, on screen or at public gatherings.

Football is the most popular sport in the world, which is why any discussion of football-related themes is generally met with great interest. This is certainly the reason why a wide range of (popular) scientific books as well as technical and subject-didactic articles have already been published on the subject. Apart from all-encompassing treatises on football, some partial aspects have attracted special interest: odd trajectories of balls (banana shots), which impressively show the Magnus effect; the high proportion of coincidence in football results which invites a statistical approach and the goalie's decisions at the penalty kick which may be explored with kinematics. However, many other, not yet discussed physical aspects of this sport may be addressed. The same applies for the over 40 forms of sports engaged in at the Olympic Summer Games.

The aim of this focus issue is to discuss the physical aspects of sports, preferably with the emphasis on football or a connection with the Olympic (Summer) Games of the present day, ensuring that they are relevant to the teaching of physics. This includes not only strictly physics considerations, but also papers which show, on the basis of sports activities, how physicists gain knowledge by means of scientific work methods.

Contributions are invited on any of the following, or related topics:

• Aerodynamics of sports projectiles
• Hydrodynamics in water sports
• Physical modelling in sport (impacts, kinematics, dynamics, biomechanics etc)
• Data analysis and visualisation in sport (using information from sensing systems)
• Statistical modelling in sport (outcome prediction, tactical simulation etc)
• The mechanics and materials of sports equipment
• Electronic and sensing systems in sport (computer vision, embedded systems)

We are looking forward to receiving many exciting submissions from you.

The first accepted contributions to the collection will be listed below, and further additions will appear on an ongoing basis.

Rod Cross 2016 Eur. J. Phys. 37 054001

Measurements are presented of the drag force on a golf ball dropped vertically into a tank of water. As observed previously in air, the drag coefficient drops sharply when the flow becomes turbulent. The experiment would be suitable for undergraduate students since it can be undertaken at low ball speeds and since the effects of turbulence are easily observed on video film. A modified golf ball was used to show how a ball with a smooth and a rough side, such as a cricket ball, is subject to a side force when the ball surface itself is asymmetrical in the transverse direction.

Rod Cross 2017 Eur. J. Phys. 38 014001

Croquet is a sport that is similar to billiards in that it involves the collision of one ball with another. Measurements and calculations are presented for three typical shots, one known as a straight croquet, one known as a split croquet and the other known as a push or roll shot. Each exhibit collision phenomena that could serve to illustrate aspects of an introductory course in mechanics, and that could also provide challenges even for more advanced students.

R De Luca and O Faella 2017 Eur. J. Phys. 38 014002

The kinematics of a free-kick is studied. As in projectile motion, the free-kick is ideal since we assume that a point-like ball moves in the absence of air resistance. We have experienced the fortunate conjuncture of a classical mechanics lecture taught right before an important football game. These types of sports events might trigger a great deal of attention from the classroom. The idealized problem is devised in such a way that students are eager to come to the end of the whole story.

T Miyazaki et al 2017 Eur. J. Phys. 38 024001

The aerodynamic properties of a spinning table tennis ball were investigated using flight experiments. Using high-speed video cameras, the trajectory and rotation of an official ball (Nittaku 3-Star Premium), which was launched by a three rotor machine, were recorded. The drag and lift coefficients ( C D and C L ) were determined by analysing the video images. The measurements covered the speed and rotation range of typical table tennis shots in the form of the Reynolds number ( Re ) and dimensionless spin rate ( SP ), i.e. 3.0  ×  10 4  <  Re  < 9.0  ×  10 4 and 0 <  SP  < 1.0, and C D and C L were obtained as functions of Re and SP . We determined that the lift coefficient C L is not a monotonically increasing function of SP . A deep valley of C L was found around SP  = 0.5, and the lift force exerted on a spinning ball almost vanished at Re  = 9.0  ×  10 4 and 0.48 <  SP  < 0.5. These results qualitatively agree with the results from recent wind tunnel tests, but quantitative differences owing to the unsteady nature of the flight experiments remain. This anomaly in the lift coefficient should be called the 'lift crisis'.

Takeshi Asai et al 2017 Eur. J. Phys. 38 024002

In downhill alpine skiing, skiers often exceed speeds of 120 km h −1 , with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s −1 , increasing to 185.8 N at 40 m s −1 . From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.

Tiago M Barbosa and Eduarda Coelho 2017 Eur. J. Phys. 38 044001

The aim was to run a case study of the biomechanics of a wheelchair sprinter racing the 100 m final at the 2016 Paralympic Games. Stroke kinematics was measured by video analysis in each 20 m split. Race kinetics was estimated by employing an analytical model that encompasses the computation of the rolling friction, drag, energy output and energy input. A maximal average speed of 6.97 m s −1 was reached in the last split. It was estimated that the contributions of the rolling friction and drag force would account for 54% and 46% of the total resistance at maximal speed, respectively. Energy input and output increased over the event. However, we failed to note a steady state or any impairment of the energy input and output in the last few metres of the race. Data suggest that the 100 m is too short an event for the sprinter to be able to achieve his maximal power in such a distance.

Rod Cross and Crawford Lindsey 2017 Eur. J. Phys. 38 044002

Measurements are presented on the drag and lift coefficients for three relatively smooth balls launched in air and tracked with two cameras separated horizontally by 6.4 m. The ball spin was varied in order to investigate whether the Magnus force would increase or decrease when the ball spin was increased. For one ball, the Magnus force increased. For another ball, the Magnus force decreased almost to zero after reaching a maximum. For the third ball, the Magnus force was negative at low ball spins and positive at high ball spins. For one of the balls, the ball spin increased with time as it travelled through the air.

John Eric Goff et al 2017 Eur. J. Phys. 38 044003

Trajectory analysis is an alternative to using wind tunnels to measure a soccer ball's aerodynamic properties. It has advantages over wind tunnel testing such as being more representative of game play. However, previous work has not presented a method that produces complete, speed-dependent drag and lift coefficients. Four high-speed cameras in stereo-calibrated pairs were used to measure the spatial co-ordinates for 29 separate soccer trajectories. Those trajectories span a range of launch speeds from 9.3 to 29.9 m s −1 . That range encompasses low-speed laminar flow of air over a soccer ball, through the drag crises where air flow is both laminar and turbulent, and up to high-speed turbulent air flow. Results from trajectory analysis were combined to give speed-dependent drag and lift coefficient curves for the entire range of speeds found in the 29 trajectories. The average root mean square error between the measured and modelled trajectory was 0.028 m horizontally and 0.034 m vertically. The drag and lift crises can be observed in the plots of drag and lift coefficients respectively.

JJ Hernández-Gómez et al 2017 Eur. J. Phys. 38 054001

Despite the impressiveness of the sprints run by Usain Bolt, the question naturally arises of why he has not been able to break the 100 m sprint world record he set in Berlin (2009). In this paper, we address such a query by considering Bolt's condition and the prevailing circumstances during the sprints that took place in Beijing 2008, Berlin 2009, London 2012, Moscow 2013, Beijing 2015 and Rio 2016 3 . Using the analytical mechanical model by Hernández-Gómez et al (2013), we analyse all the events, equating what we thought were the principal factors a priori : tailwind, weight gain and age. Despite what one might expect about the role of age in such a high-performance athlete as Usain Bolt, our results show that his performance has been essentially constant from Beijing 2009 to Rio 2016, with the mass gain and tailwind conditions making the difference in the run times he has achieved since Berlin 2009. Actually, our analysis suggests that in equal mass and tailwind conditions, his world record could actually have been set at Beijing 2015.

T Miyazaki et al 2017 Eur. J. Phys. 38 064001

The aerodynamic properties of an arrow (A/C/E; Easton) were investigated in an extension of our previous work, in which the laminar-turbulent transition of the boundary layer on the arrow shaft was found to take place in the Re number range of 1.2  ×  10 4  <  Re  < 2.0  ×  10 4 . In this paper, we focus on the influence of the arrow's attitude on the transition. Two types of vane (Spin Wing vane and Gas Pro vane) are fletched, and their stabilizing effects are compared. Two support-interference-free tests are performed to provide aerodynamic properties such as the drag, lift and pitching moment coefficients. The static aerodynamic properties are measured in a wind tunnel with JAXA's 60 cm magnetic suspension and balance system. When the arrow is aligned with the flow, the boundary layer remains laminar for Re  < 1.5  ×  10 4 , and the drag coefficient is approximately 1.5 for 1.0  ×  10 4  <  Re  < 1.5  ×  10 4 . If the arrow has an angle of attack of 0.75 ° with the flow, the transition to turbulence takes place at approximately Re  = 1.1  ×  10 4 , and the drag coefficient increases to approximately 3.1. In addition, free flight experiments are performed. The arrow's velocity and angular velocity are recorded using five high-speed video cameras. By analysing the recorded images, we obtain the initial and final velocities from which the drag coefficient is determined. The trajectory and attitude of the arrow in free flight are computed numerically by integrating the equations of motion for a rigid body using the initial data obtained from the video images. The laminar-turbulent transition of the boundary layer is shown to take place, if the maximum angle of attack exceeds about 0.4° at Re  = 1.75  ×  10 4 . The crucial influence of the initial angular velocity on the angle of attack is also examined.

Panos J Athanasiadis 2018 Eur. J. Phys. 39 014002

Slacklining is a new, rapidly expanding sport, and understanding its physics is paramount for maximizing fun and safety. Yet, compared to other sports, very little has been published so far on slackline dynamics. The equations of motion describing a slackline are fundamentally nonlinear, and assuming linear elasticity, they lead to a form of the Duffing equation. Following this approach, characteristic examples of slackline motion are simulated, including trickline bouncing, leash falls and longline surfing. The time-dependent solutions of the differential equations describing the system are acquired by numerical integration. A simple form of energy dissipation (linear drag) is added in some cases. It is recognized in this study that geometric nonlinearity is a fundamental aspect characterizing the dynamics of slacklines. Sports, and particularly slackline, is an excellent way of engaging young people with physics. A slackline is a simple yet insightful example of a nonlinear oscillator. It is very easy to model in the laboratory, as well as to rig and try on a university campus. For instructive purposes, its behaviour can be explored by numerically integrating the respective equations of motion. A form of the Duffing equation emerges naturally in the analysis and provides a powerful introduction to nonlinear dynamics. The material is suitable for graduate students and undergraduates with a background in classical mechanics and differential equations.

Adrian L Kiratidis and Derek B Leinweber 2018 Eur. J. Phys. 39 034001

Drag and lift coefficients of recent FIFA world cup balls are examined. We fit a novel functional form to drag coefficient curves and in the absence of empirical data provide estimates of lift coefficient behaviour via a consideration of the physics of the boundary layer. Differences in both these coefficients for recent balls, which result from surface texture modification, can significantly alter trajectories. Numerical simulations are used to quantify the effect these changes have on the flight paths of various balls. Altitude and temperature variations at recent world cup events are also discussed. We conclude by quantifying the influence these variations have on the three most recent world cup balls, the Brazuca, the Jabulani and the Teamgeist. While our paper presents findings of interest to the professional sports scientist, it remains accessible to students at the undergraduate level.

Lazar Radenković and Ljubiša Nešić 2018 Eur. J. Phys. 39 034002

The main contribution of this paper is didactic adaptation of the biomechanical analysis of the three main lifts in powerlifting (squat, bench press, deadlift). We used simple models that can easily be understood by undergraduate college students to estimate the values of various physical quantities during powerlifting. Specifically, we showed how plate choice affects the bench press and estimated spine loads and torques at hip and knee during lifting. Theoretical calculations showed good agreement with experimental data, proving that the models are valid.

Agam Shah et al 2018 Eur. J. Phys. 39 044001

The kinematics and dynamics of projectiles in sports is a complex topic involving several physical quantities and variables such as time, distance, velocity, acceleration, momentum, force, energy, viscosity, pressure, torque, bounce, sliding, rolling, etc. The analysis of these complex sets of multidimensional information, including the correlation between different variables, is an important requirement for the clear understanding of projectile trajectories in sports. However, those who do not have a strong mechanics or physics background find it difficult to interpret the data and comprehend the results in terms of the interacting forces and mutual interaction, which perpetuate the motion of the ball (or projectile). To address this issue, we propose a novel multivariate-data-visualization-based understanding of projectiles in sports inspired by the basic Gestalt principle that the whole is greater than the sum of its parts. The data representation approach involves the use of a single two-dimensional plane for the representation of multidimensional dynamic variables, and thereby completely removes the requirement of using several 2D plots for analysing and comprehending the meaning behind all of the data and how it correlates. For this study, we have considered the dynamics of two ball sports, namely volleyball and table tennis, as well as the sport of badminton, which involves high-drag projectile motion. We have presented a basic computational model incorporating the important forces to study projectile motion in sports. The data generated by the simulation is investigated using the proposed visualization methodology, and we show how this helps it to be interpreted easily, improving the clarity of our understanding of projectile trajectories in sports using both force and energy language.

Wolfgang Püschl 2018 Eur. J. Phys. 39 044002

This article is to review, for the benefit of university teachers, the most important arguments concerning the theory of sailing, especially regarding its high-speed aspect. The matter presented should be appropriate for students with basic knowledge of physics, such as advanced undergraduate or graduate. It is intended, furthermore, to put recent developments in the art of sailing in the proper historic perspective. We first regard the general geometric and dynamic conditions for steady sailing on a given course and then take a closer look at the high-speed case and its counter-intuitive aspects. A short overview is given on how the aero-hydrodynamic lift force arises, disposing of some wrong but entrenched ideas. The multi-faceted, composite nature of the drag force is expounded, with the special case of wave drag as a phenomenon at the boundary between different media. It is discussed how these various factors have to contribute in order to attain maximum speed. Modern solutions to this optimisation problem are considered, as well as their repercussions on the sport of sailing now and in the future.

André Seyfarth and Christian Schumacher 2019 Eur. J. Phys. 40 024004

Our daily activities involve different types of locomotion, including walking and running. In this paper we present a series of biomechanical models to describe such locomotor activities with a set only a few characteristic parameters. With this we aim at providing an introduction to the modelling of human locomotion which is equally appropriate for high-school and university-level students. We share our experiences with integrating these biomechanical models into classes with students of different disciplines comprising engineering, computer science, physics and sport science. Supplementing these modelling approaches, we use experimental methods as well as robotic testbeds to evaluate and justify the biomechanical simulation models. By this, we enable students from different fields to gain first experiences in the understanding and application of human movement systems and potential extensions to related technologies, such as robotics and assistive devices (e.g. prostheses and exoskeletons).

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• Copy URL https://www.pbs.org/newshour/science/the-not-so-hidden-physics-of-your-favorite-olympic-event

The not-so-hidden physics of your favorite Olympic event

No matter how high an Olympian jumps, how fast they run, how hard they kick a ball, their amazing feats are always governed by the laws of physics. Pushing the physical limitations of a sport, as the world’s best athletes do, isn’t about breaking those laws but knowing just how far to bend them to their competitive advantage.

“When I’m watching a sporting event, I can’t help but look at it through the lens as a physicist — I’m watching the way the arms are moving, the twists and the turns,” said University of Lynchburg physicist Eric Goff.

But you don’t need a PhD to wrap your head around the basic rules that dictate sports, and well, everything. All you really need is a refresher on some of the basic principles you may have learned back in grade school science class.

Here’s a crash course on how to see those key laws in action.

How physics rules the Games

Long before the first modern Olympics, English scientist Sir Isaac Newton identified three basic laws of motion.

Graphic by Megan McGrew/PBS NewsHour

In the world of sports, there are plenty of examples that illustrate Newton’s first law — an object will stay either in motion or at rest until a force acts upon that object to change it. Jahred Adelman, associate professor of physics at Northern Illinois University, said. When a volleyball player dives for a ball, for instance, that player won’t stop moving until something else applies a force to stop them — in this case, the hard surface of the court.

“Once you start moving, you keep moving,” Adelman said. “And if you’re not moving, you’re not magically going to start moving unless you do something — [like] take a leap.”

When it comes to Newton’s second law, captured by the equation “force equals mass times acceleration,” look no further than the track. We know from his first law that in order for an object — like a person — to start moving, a net force must get it going. Net refers to the sum of all forces acting on an object, Adelman explained.

Sprinters at rest need a force to kick off their acceleration. They find that force not just with their own bodies but by pushing against starting blocks.

A sprinter “wants as large of an acceleration as possible, and she can’t change her mass on the starting blocks,” Adelman said. “So to make the acceleration as big as possible, she wants to have as large of a net force as possible.”

That’s why sprinters push off as hard as they can against the blocks, Adelman added, in an example of Newton’s third law — the greater that force is, the greater the opposite force enacted by the starting block will push them forward.

Newton’s third law turns up in rowing to illustrate how exactly boats travel forward. Rowers use as much force as possible through their oars to push the water. That water, in turn, pushes back on the boat with equal force, propelling the vessel forward.

With those basics in mind, let’s dive a little deeper into some signature moves.

When you’re watching the world’s top gymnasts compete, keep an eye on their arms for an example of the law of conservation of angular momentum. The laws of physics stay the same even when an object changes angles, Adelman said.

When an athlete launches themselves into the air, their angular momentum will remain constant, or conserved. But if they move their bodies to change how their mass is distributed, they can manipulate the speed of their rotation.

“That’s why you will see [gymnasts] shift their arms in different directions — they put their arms out or put their arms close to their body — because that changes how their mass is distributed,” Adelman explained. “And then to conserve angular momentum, their body then has to rotate differently.”

Simply put: The farther a gymnast’s arms are from their body, the slower they’ll rotate. But when they bring their arms close to their core, they’ll rotate faster.

A faster spin allows gymnasts to pull off the complex series of twists involved in their routine in time to land safely on the ground. At the end of their performance, you’ll see their arms spread out.

“That’s not only because it looks good for the judges, but that also helps slow down their rotation because they’re landing after a long set of twists, and they don’t want to keep twisting and fall backwards,” Adelman added. “The more mass is distributed far away from their body, the more they will slow down their rotation.”

Rarely does an athlete debut an innovative move that completely changes how future generations approach the sport. But during the 1968 Summer Olympics, that’s exactly what high jumper Dick Fosbury did with his gold-winning “Fosbury Flop,” which helped him leap 7 feet and 4.25 inches and set an Olympic record.

In the high jump, the goal for athletes is to reach the highest height possible while jumping over a pole without knocking it over.

Ian Hume uses a scissor kick in 1979. Photo by Erin Combs/ Toronto Star via Getty Images

Prior to Fosbury, high jumpers would use techniques like the “ scissor kick ” that force their center of mass, or the average position of their body, to pass over the bar, which they faced head-on. They threw themselves over in something closer to an upright position.

Regardless of technique, the maximum height that a high jumper’s center of mass can reach is established as soon as they leap off the ground, Goff explained.

The tricky thing about that average position of an object is that it doesn’t have to be located on an object itself. The center of mass of a donut, for example, is the empty hole in the middle, Goff said. The pastry is wrapped around its center of mass.

The Fosbury Flop is sort of like bending your body into a donut shape in order to manipulate your own center of mass. By jumping head first and arching his body upward, Fosbury moved his center of mass under the bar and made his jump more efficient.

“The Fosbury Flop allows a jumper to clear a bar height that’s greater than the maximum height of the jumper’s center of mass, which was not possible with the scissor technique,” Goff said.

Have you ever watched a soccer player kick a ball that seems to magically change direction in the air, scoring a seemingly impossible goal?

That’s not magic — it’s the Magnus effect. Kicking the ball at a certain angle allows it to spin, which is crucial for setting up its trajectory to change as it’s moving in the air.

As that spinning soccer ball is traveling in one direction, some air is traveling in the same direction of the spin, and appears to have a velocity equal to the ball’s speed plus its spin speed, Adelman explained. On the other side, air is moving in the opposite direction, and its velocity appears to be equal to the ball’s speed minus its spin. The relative air speed, therefore, is larger on the side that’s spinning with the ball. Those differing speeds act as two different forces on each side of the ball.

Why does that difference matter? There’s a drag force between the ball and the air that depends on the relative air speed, Adelman said. The faster that speed, the more drag force there is. Newton’s second law indicates that when there is a non-zero force, the ball must accelerate in the direction of that force.

Goff offered the example of a right-footed kicker approaching a ball for a corner kick. If that player aims their foot to the right of the ball’s center, their kick can exert torque that creates “a counterclockwise rotation on the ball.”

As the ball flies through space, air whips off its back. In an example of Newton’s third law — which involves actions and equal and opposite reactions, if the ball pushes air to the right, that air must push it back to the left.

“In addition to a normal drag force on the ball, which acts opposite the ball’s velocity, the ball experiences a sideways force to the left [from the player’s perspective,]” Goff said. “That sideways force causes the ball to be deflected to the kicking player’s left.”

So the next time you see a soccer player make a ball swerve at the perfect moment, remember this phenomenon and all the ways the laws of physics can play to your advantage.

Bella Isaacs-Thomas is a digital reporter on the PBS NewsHour's science desk.

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Physics of Sports

• First Online: 25 August 2020

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This chapter provides an overview of physical principles used in modern sport science. In addition to physics, kinesiology, and biomechanics, we will also discuss how deep learning can help a sport data scientist, and vice versa, how we can improve our models by knowing a few physics principles. Classical mechanics is a reliable method of movement analysis, and it’s a valuable tool if you’re planning to build any practical sport machine learning models. In this chapter, I’ll show how machine learning models, including neural nets and reinforcement learning, can be applied to biomechanics.

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Ashley, K. (2020). Physics of Sports. In: Applied Machine Learning for Health and Fitness. Apress, Berkeley, CA. https://doi.org/10.1007/978-1-4842-5772-2_2

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• 31 March 2021

Sports science

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The competition to be crowned the fastest, strongest or most technically proficient sportsperson on the planet will once again reach its peak this summer when athletes descend on Tokyo for the Olympic Games. The global pandemic might rule out the throng of enthusiastic spectators that are typical of such an event, but millions will eagerly watch on television as the very best go toe-to-toe.

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Understanding simple physics in sports

Physics and sports are inter-connected. Every sports discipline depends on the ability of an athlete in force application, and force is one of the key elements of Newton’s Laws and other fundamental physics concepts.

Published : Dec 14, 2021 15:18 IST

Physics in sports: Understanding the physics of motion can impact all areas of sports, from helping athletes to move faster, further and higher, injury prevention, programme planning and peaking at the right time.

Some of the common terminology we use day today in sport have become a part of the coaching jargon. We will look at some of the examples, their real meaning and how they are being applied in different sports.

A good performance in sports is based on correct control and coordination of movements. Using physics as one of the medium to understand the subject better we will discuss the physics terms used in various sports. For example, knowing the bat speed with which to strike a ball isn’t very useful to a batter, but what is useful is knowing the swing angle to stabilise your wrists so that the bat hits the ball with the greatest speed possible.

Understanding the physics of motion can impact all areas of sports, from helping athletes to move faster, further and higher, injury prevention, programme planning and peaking at the right time.

Along with force, work and energy are among the most important concepts of physics. Both work and energy play an imperative role in sports which is directly proportional to each other — transfer of work and energy from one place to another and from one form to another.

Speed: is the time rate at which an object is moving along a path. Ex: sprinting or chasing a ball or target is a scalar quantity.

Velocity: the rate at which the body is moving in a particular direction. Ex: car moving in a westward direction is a vector quantity.

Acceleration: rate at which velocity changes with time, in terms of both speed and direction. Ex: player running at 10mts/sec towards west, chasing the ball.

Momentum: product of mass of a body and its velocity = mass*velocity.

In contact sports, the more momentum a player has, the more harder it is to stop him or her. Ex: rugby or rules football or basketball players.

Inertia: tendency of an object to continue in the state of rest or of uniform motion. Ex: if you roll a ball, it will be in a rolling motion unless stopped by friction or some force (billiards or soccer ball).

There are three types of inertia — resting, motion and directional.

Angular momentum: the movement of a mass when it is rotating or spinning. A person in a tucked position spins faster than someone in an extended position. In general, the larger the angular momentum of the ball, the larger its linear velocity. Ex: baseball pitching or a fielder throwing a ball to the keeper. This maximises the angular momentum of the throwing arm and of the ball at release.

Deceleration: the rate at which an object slows down. Ex: when we are using brakes during driving, we are taking benefits of deceleration to reduce the speed of the vehicle, especially in stop and go sports.

Torque : is a twisting force that involves the muscles rotational force and measures how much of that twisting force is available when an muscle exerts itself. Ex: fast bowlers’ action or tennis strokes or golf swing. Torque-based gym training is very useful for professional sportsmen — rotating your arms and legs into stable positions before and during movement. Torque is a moment that is applied in such a way that it tends to rotate a body around its axis.

Ground reaction force (GRF) : this has three components: its point of application, its magnitude, and its line of action. In the stance phase of normal gait, the point of application progresses along the foot, and the magnitude and the line of action vary through the gait cycle. Ex: while running, the GRF increases up to two or three times the body weight.

Angle of release: ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45° . If air resistance is taken into consideration, the ideal angle is somewhat less than 45°. Ex: discus, shot put or javelin throws.

Couple: pair of equal parallel forces that are opposite in direction. Ex: steering wheel of a car.

Force: is a push or pull upon an object resulting from the object’s interaction with another object. In sport it can be force creation or force dissipation and can be achieved through various parameters of training the right muscle group. In sport, an internal force is one which is generated within the body. Ex: leg muscles contracting to move the bones. An external force is one that acts outside the body. Ex: a boxer striking an opponent.

In every ball game, a force applied to the ball makes it move, whether from the kick of a footballer or the action of a tennis racquet. In motor sports, force make the vehicles move, and other forces are needed to stop them. Hammer throwers and American footballers make use of force to run and throw.

Levers in the body

First class lever: the fulcrum is in the middle of the effort and the load. Ex: neck flexion and extension

Second class lever: the load is in the middle, between the fulcrum and the effort.. Ex: calf raise

Third class lever: the effort is in the middle, between the fulcrum and the load. Ex: biceps curl.

Newton’s laws

First law: a body continues in a state of rest or uniform velocity unless acted upon by an external force. Ex: a golf ball will remain still unless a force, applied by the golf club, makes it move. Or the same golf ball will continue to move at a constant velocity unless a force acts on it to slow down.

Second law: when a force acts on an object, the rate of change of momentum experienced by the object is proportional to the size of the force and takes place in the direction in which the force acts. Ex: when a golf ball is struck by the golf club, the rate of change of momentum (or velocity) of the ball is proportional to the size of the force acting on it by the club.

Third law: for every action, there is an equal and opposite reaction. Ex: when a tennis player hits a ball, the racquet exerts a force on the ball and the ball exerts an equal and opposite force on the racquet. The racquet exerts the action force and the ball exerts the reaction force which is felt by the player at the time the racquet strikes the ball.

Kinetic energy: when work is done on an object, the object gains speed and acquires kinetic energy. When a player throws a ball, work is done. The arm applies a force to the ball through a distance. Ex: when you hit a ball with a bat or racquet, work is done.

Potential energy : an object can store energy as the result of its position. Ex: the heavy bat is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position.

Impulse : it is a certain amount of force you apply for a certain amount of time to cause a change in momentum. Ex: when you hit a ball with a cricket bat, you apply a force for a time (a very short period in this case) to cause a change (or transfer) of momentum in the ball.

Balance and stability : balance is the ability to stay upright or stay in control of body movement, and coordination is the ability to move two or more body parts under control, smoothly and efficiently. There are two types of balance: static and dynamic. balance is established by four different body systems — vestibular system, vision, proprioceptors, and the hip and trunk muscle group. Each can be trained through varied means to achieve the desired results.

Mechanics : mechanics is a branch of physics that is concerned with the description of motion/movement and how force creates motion or movement.

Use of biomechanics is as follows

• identifies how the muscular and skeletal systems in humans function under various conditions.
• understands the limits of the human body through various mathematical and physical formulae.
• improves athletic performance by identifying and applying optimal technique.
• individualises performance domain.
• prevents injury and speeds up recovery.
• increases movement speed.
• increases power.
• efficient economy of movement.
• eliminates muscle imbalances.
• diminishes wear and tear on joints and ligaments.
• improves sport and skill specific form and technique.

Drag: every time we move, we have to push millions of air or water molecules out of the way, which slows us down. It can be air or water drag. Depending on the sport, the drag can be form drag, interference drag or skin friction drag. Ex: speed skating or swimming.

Spin: is created by applying a force that is off-centre to the object being thrown (or kicked) at the point of release. The effects of spin are important in all ball sports and throwing events. The magnus effect explains why the paths of balls deviate from normal flight path. Ex: cricket, soccer or golf ball.

Mass: the mass of a body refers to the amount of substance that it is made up of and is measured in kilograms (kg). If a player weighs 100kg, he or she is made up of bones, muscle, fat, connective tissue, etc. Although we talk about a player’s ‘weight’ on scales, weight is a force. If the same player is placed on the moon his/her mass would still be 100kg but the weight would be much less because the gravity is less.

Using the knowledge of physics and other science parameters would vary for different coaches. Understanding the data inference to specific sport and specific athlete and skill to peak at the right time is an art.

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On-Campus Summer Programs

The physics of sports.

• Grades 7-11
• Residential
• Science and Engineering

How does a pitcher get a baseball to curve mid-pitch? Why does an ice skater spin faster when she pulls in her arms? How can Tony Hawk land a “900,” a skateboard trick involving the completion of two-and-a-half aerial revolutions? Physics holds the key to answering these and other fascinating sports questions. This introductory physics course uses sports to explore mechanics: kinematics, dynamics, momentum, energy, and power. You’ll experiment with billiard balls to investigate collisions and conservation of momentum, study centripetal forces to determine how fast a racecar can take a turn, and use kinematics and projectile motion to discover the best angle from which to shoot a basketball. You and your classmates will explore the real-world applications of physics concepts in sports through lectures, hands-on activities, labs, simulations, mathematical problem sets, and research projects. Along the way, you’ll develop a strong understanding of the principles that give star athletes an edge over their competitors.

Typical Class Size:  16-18  

Course Overview

Learning Objectives:

• Construct a model of Newtonian mechanics from a sport of your choice presenting relevant physics concepts
• Analyze and solve mathematical computations in kinematics, momentum, energy loss, and impulse in colliding systems in sports
• Integrate and apply physics concepts conservation, work, energy, and power to a sport to produce a plan to improve efficiency and performance in sports

Summer Dates & Locations

After May 31, 2024 , registration is available upon request pending eligibility and seat availability. To request placement, email [email protected] after submitting a program application.

Session One

Session Two

Testing and prerequisites.

Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.

Cost and Financial Aid

Application fee.

• Nonrefundable Application Fee - $50 (Waived for financial aid applicants)
• Nonrefundable International Fee - $250 (outside US only)

Financial Aid

We have concluded our financial aid application review process for 2024 On-Campus Programs. We encourage those who may need assistance in the future to apply for aid as early as possible.

Course Materials

Students should bring basic school supplies like pens, notebooks, and folders to their summer program. You will be notified of any additional items needed before the course begins. All other materials will be provided by CTY.  

Course Extras (Lab fee info, etc): Lab fee: $145

Sample Reading

These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.

• The Physics of Sports , Michael Lisa

About Science and Engineering at CTY

Explore space and our planet.

In our Introduction to Astronomy course, we’ll visit a nearby observatory or planetarium, see what the cosmos looks like through various spectra, and immerse ourselves in the science and technology that bring the universe closer to home. In Marine Ecology , we’ll visit local wetlands and tidepools, observe flora and fauna, collect water samples and analyze them for clues about their health and humans’ impact. And in The Global Environment , we will explore the human impact on our environment and generate proposals for addressing climate change.

Bond over chemistry

Our chemistry courses help you see the world differently, starting at the atomic level. The Edible World gives budding chefs and science lovers a glimpse into the chemical reactions that happen when we make food, and the chemical makeup of meals and treats we eat every day. In our Crystals and Polymers course, we’ll synthesize slime, grow rock candy, and isolate strawberry DNA to learn about the molecular structure of naturally occurring gems and human-produced plastics. In Chemistry in Society , we'll consider how the chemicals in products can both enhance and degrade the world around us; produce biodiesel in a lab to understand alternative fuels; and prepare aspirin to learn about the healing and toxic properties of pharmaceuticals.

Meet our instructors and staff

CTY is one of the highlights of my year. Even though it’s the summer, the immersive learning in a subject where these students truly excel and shine is invigorating for me as a teacher.

Lauren LaPorta

Writing Instructor

My favorite thing about teaching at CTY is watching the students' curiosity and excitement lead their learning. It's exciting as an instructor to witness their confidence increase and watch as their 'aha' moments manifest into increased knowledge and mastery of the content.

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Robotics Instructor

The students are so bright, interesting, and often willing to try some of the most silly and unique activities that the RAs create.

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Essay on Importance of Sports for Students and Children

500+ words essay on importance of sports.

First of all, Sport refers to an activity involving physical activity and skill . Here, two or more parties compete against each other. Sports are an integral part of human life and there is great importance of sports in all spheres of life. Furthermore, Sports help build the character and personality of a person. It certainly is an excellent tool to keep the body physically fit. Most noteworthy, the benefits of Sports are so many that books can be written.  Sports have a massive positive effect on both the mind and body.

Physical Benefits of Sports

First of all, Sports strengthen the heart. Regular Sports certainly make the heart stronger. Hence, Sport is an excellent preventive measure against heart diseases . This certainly increases the life expectancy of individuals. Furthermore, a healthy heart means a healthy blood pressure.

Sports involve physical activity of the body. Due to this physical activity, blood vessels remain clean. Sports reduces the amount of cholesterol and fats in the body. This happens because of the increase of flexibility of the wall of the blood vessels. The flexibility increases due to physical exertion, which is the result of Sports.

Furthermore, the sugar level in blood also gets lower thanks to Sports. The sugar certainly does not accumulate in the blood due to physical activity.

Get the huge list of more than 500 Essay Topics and Ideas

A person experiences a good quality of breathing because of Sports. Sports strengthen the lungs of the body. Sports certainly escalate the lung capacity and efficiency of the body. Hence, more oxygen enters the blood which is extremely beneficial. Furthermore, there are fewer chances of developing lung diseases due to Sports.

Appropriate body weight is easy to maintain because of sports. A Sports playing person probably does not suffer from obesity or underweight problems. Sports certainly help the body remain fit and slim.

Furthermore, Sports also improves the quality of bones. A person who plays sports will have strong bones even in old age. Several scientific research reports that Sports prevent many diseases. For example, many researchers conclude that Sports prevent the development of cancer.

Other Benefits of Sports

Sport is certainly an excellent tool to build self-confidence . Playing Sports increases confidence to talk properly. A sport certainly improves the skills of communicating with others. Furthermore, the person experiences confidence in sitting, standing, and walking properly. Hence, Sports enriches the social life of an individual.

Sports bring discipline in life. It certainly teaches the values of dedication and patience. Sports also teach people how to handle failure. Furthermore, the importance of following a time schedule is also present in Sports.

Above all, Sports improves the thinking ability of individuals. Sports certainly sharpen the mind. Children who play Sports probably perform better at exams than those who don’t.

Finally, Sports reduces the stress of mind . A Sports playing person would certainly experience less depression. Sports ensure the peace of mind of those playing it. Most noteworthy, Sports brings happiness and joy in the life of individuals.

A sport is an aspect of human life that is of paramount importance. It certainly increases the quality of human life. Sports must be made mandatory in schools. This is because it is as important as education. Everyone must perform at least one Sport activity on a regular basis.

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Explained: If Olympic sports were everyday life

• Zenia D'Cunha

The Olympics are upon us and it's that time again, when we enjoy the superhuman sporting acts of elite athletes from the comfort of our screens. And perhaps wonder, just how much physical strain their bodies have to bear to run, swim, jump, throw or hit better than everyone else.

The sheer defiance of physics when gymnast Simone Biles rotates her body in mid-air or when weightlifter Mirabai Chanu lifts four times her body weight or when pole vaulter Mondo Duplantis leaps over 20 feet in the air. What would it be like if we laypeople had to put in physical effort equivalent to that of an Olympian is our daily life? Facing a smash that comes in faster than bullet trains or jumping off the third floor without any support.

We tried to understand how Olympic sports would be like in everyday life:

Javelin throw

AKA the Neeraj Chopra sport we Indians are very familiar with by now. The javelin weighs 800 gm and is about 8 feet.

Imagine hurling three cricket bats (end-to-end) that weigh a little more than a Cola PET bottle (the 750ml sized ones...) so far that it would cross 90 floors of a skyscraper on its side (or two India Gates).

10m air rifle - Shooting

The sport that has won India two Olympic medals, including that precious first ever Olympic gold by Abhinav Bindra. The rifle used in the discipline weighs about 5.5kg and the bull's eye ring on the target is 0.5 mm.

Imagine you hold 6 laptops steady at shoulder height, and hit a target the size of the nib of a pen from a distance that's about the length of a full-sized school bus. Repeatedly. 60 times. While wearing a tight-fitted jacket and trousers that weigh about 1-2 kg themselves. Oh, and the laptops recoil back (a bit) with each shot.

Bonus: A 10m air pistol is about 1.49 kg and it has to be held aloft in one hand, straight and steady. Imagine carrying home your groceries from the market like that.

Dragflick - Hockey

Imagine a rock travelling at around the speed of a Vande Bharat Express train coming straight at you.... and instead of dodging it, you run towards it. Hoping it hits you. So you can stop it.

That's the job of the rushers as they try to stop the dragflicker trying to convert the penalty corner. And there are multiple PCs in a match, with the rules very fluid on what transgression demands a PC and what doesn't.

Imagine the Great Khali standing his full 7 feet 1 inch tall (2.15m) in your path, and you take a short sprint and flop your entire body over him, without touching him. That's what high-jumpers do on the regular and then some. The world record stands at 2.45m and India's national record at 2.29m, so maybe it's the Great Khali with a mohawk.

Smash - Badminton

We must have all played badminton at some point, but very few would have seen the shuttle coming at you faster than a bullet train, airplane or even a Formula 1 car. Much faster. Because the fastest smash recorded in badminton, both in game and in monitored environments, belongs to one Indian - Satwiksairaj Rankireddy - and it's at an unimaginable speed.

The Indian doubles star has hit a smash 500 km/h during a match and raised that to a fast and furious 565 km/h while at the Yonex facility with the aim of breaking the world record. For comparison, the fastest cricket ball is 161.3 km/h, the fastest tennis serve is 263 km/h and the fastest F1 car speed is 397.36km/h. Satwik is way ahead of that.

Fun fact: Three Indians top the recent list of fastest smashes on BWF Tour, with singles players Lakshya Sen and HS Prannoy around the 419 and 420 km/h mark. Both will be making Olympic debuts at Paris 2024.

The average height of hurdles in the 100m - where Jyothi Yarraji will be competing - is 3.5 feet. Imagine running full tilt to catch a flight and having to leap over an airport trolley not once, but 10 times back-to-back.

There's no Indian representation in this sport but it's still a fascinating watch.

Imagine jumping off what is the third floor of a building (10 meters) to hit the water as a speed of about 56.3 km/h and doing it while holding perfect form or moving in precise choreography mid-air and sometimes even synchronising with another human.

Weightlifting

A sport where success depends on lifting four times your body weight, 6 times for a medal and countless times daily in training. It will put any gym deadlift video to shame.

Take Mirabai Chanu, the silver medallist in women's 49 kg weightlifting, for example. Mirabai's daily total works out to 12,000 kg, which is the weight of five Mercedes G Wagons, or a 17-foot six-wheeler truck.

(For context: Virat Kohli's bat weighs around 1.2kgs. For him to be able to lift as much weight as Mirabai in a day, he would have to face 10,000 deliveries; Kohli played a total of 3072 deliveries in 2023.)

Boxing (heavy weight)

Taking one punch in heavyweight boxing is the equivalent of getting hit by a 5 kg sledgehammer swung from over-the-head. It generates as much power as a hatchback (think i-20 or Altroz).

Scientists say Sha’Carri Richardson can run on water. Just… maybe not in Paris.

Scientists theorize that the Olympic sprinter has what it takes to run atop the surface of the water somewhere in the universe.

The superlatives have been flying for Sha’Carri Richardson in advance of the Paris Olympics . Fastest woman in the world. Gold medal favorite.

Richardson could possibly even flirt with the 100-meter dash world record, set over 30 years ago by Florence Griffith-Joyner.

But could Richardson also break the laws of physics?

According to a hypothesis in Runner’s World , the surprising answer is “Yes…elsewhere in the solar system.”

Get off the sidelines and into the game Our weekly newsletter is packed with everything from locker room chatter to pressing LGBTQ sports issues. Weekender * Weekly Newsletter * Promotions and Partner Emails * Sign Up

Correspondent Laura Ratliff pondered whether it was possible for an elite runner like Richardson to achieve a sprint speed so fast that she could run on water. 

Literally, not metaphorically.

That would be an all timer of a sports moment, especially considering that the last beat writers to cover this feat were Matthew, Mark, Luke and John.

Ratliff’s article detailed how Harvard researchers Tom McMahon and Jim Glasheen formed a mathematical model to determine the conditions necessary for a human to pull this off by studying the Basilisk lizard , a species that is able to run atop water to evade predators.

It’s become customary to compare Richardson to some of the fastest inhabitants on the planet. Comparing her to them on another planet is a new one.

There was a lot of math in the study, but basically what McMahon and Glasheen determined was that a human sprinter would need to achieve a speed of 98 feet per second in order to support their weight on the surface of the water. Not even Richardson could do that.

Sadly, holding the 100m Finals on the Seine wouldn’t give Richardson an edge. 

On Earth anyway.

Related Sha’Carri Richardson is Outsports 2023 Female Athlete of the Year Sha’Carri Richardson is an out LGBTQ athlete and the world’s fastest woman, with her sights on Olympic gold. By Jim Buzinski | December 19, 2023

However, a 2012 study at the University of Milan determined that humans could briefly support their own weight on top of a liquid body in an environment with 10% of Earth’s gravity.

This led Physics World’s Nicole Sharp to present a theory . Jupiter’s moon Titan has 13.8 percent of Earth’s gravitational acceleration and features lakes consisting of frigid ethane and methane.

“To stay atop Titan’s ethane, Richardson would have to slap the surface at about 9.0 m/s…Her world championship time was significantly faster at 9.3 metres per second,” Sharp wrote.

Of course, the average surface temperature on Titan is -300 degrees Fahrenheit. So there’s that.

Still, if you move the Olympics to Titan, Richardson would be the first athlete to win a 100m dash with a time similar to Florence Griffith-Joyner and a short program score comparable to Tara Lipinski.

After which she could add “actual miracle worker” to her bio.

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Gymnast ‘rigorously’ tests beds at Paris Olympics, where condoms want you to share ‘victory’

Ireland’s Rhys McClenaghan has again debunked the myth that the Olympic beds are ‘anti-sex’ while the Paris 2024 condoms carry messages.

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Manchester United consider offering Aaron Wan-Bissaka to Inter Milan in exchange for Denzel Dumfries - Paper Talk

Plus: Man Utd eye Benfica's Antonio Silva as cut-price alternative to Jarrad Branthwaite; United also hold interest in ex-Liverpool star Neco Williams; Aston Villa reject improved West Ham offer for Jhon Duran; Sam Lammers edges closer to Twente move; Jakub Kiwior ready to leave Arsenal

Thursday 25 July 2024 23:26, UK

The top stories and transfer rumours from Friday's newspapers...

Manchester United are considering offering Aaron Wan-Bissaka to Inter Milan in exchange for Denzel Dumfries.

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Steve McClaren has not travelled to the US with Manchester United for their pre-season tour.

Ivan Toney's Brentford exit is in doubt after his replacement Igor Thiago suffered an injury, with West Ham and Tottenham in the hunt for the 28-year-old.

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• Latest News

Bordeaux have chosen to renounce their professional status after being relegated to the third tier.

Rangers face a two-way race with FC Copenhagen to sign Manchester United academy star Hannibal Mejbri, according to a report.

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England's stars have paid tribute to Gareth Southgate in a heartfelt video following his decision to quit his role as senior team manager.

Pep Guardiola claimed his love for the job has kept him going into a ninth year at Manchester City in comments that will give supporters hope of a longer stay.

Aston Villa have rejected West Ham's improved offer of £32m plus 18-year old midfielder Lewis Orford for striker Jhon Duran.

Jarrad Branthwaite is not intending to sign a new deal at Everton unless they can match the £160,000-a-week being offered by Manchester United.

Manchester City are hopeful that any ban handed to Rodri for an inflammatory chant during Spain's European Championship celebrations will not impact their Champions League campaign.

Aston Villa are monitoring developments with Borussia Dortmund's Karim Adeyemi.

DAILY MIRROR

Reece James admits that he still has a lot to learn in his new role at Chelsea under boss Enzo Maresca.

Jakub Kiwior is ready to leave Arsenal as they prepare to welcome £42m signing Riccardo Calafiori.

THE ATHLETIC

Tottenham Hotspur have agreed a deal to sign South Korean winger Yang Min-hyuk from Gangwon FC.

Nottingham Forest and Crystal Palace have been warned about their commercial relationship with shirt sponsors Kaiyun Sports, after it emerged that the betting website is not licensed to trade in the UK.

Watford are in advanced talks over the signing of Fluminense left centre-back Kayky Almeida.

Newcastle United coach Ben Dawson has left to join Leicester City, ending a 10-year association with the club.

Leeds United have had a bid for Koln midfielder Dejan Ljubicic rejected.

St Johnstone youth defender Callan Hamill has travelled with Arsenal's under-18 squad for pre-season but is facing a decision on his future as Celtic have tabled a contract offer.

DAILY TELEGRAPH

Manchester United's academy staff have been left "shocked", "upset" and in some cases "angry" at the news that several respected, long-serving coaches could lose their jobs in the cost-cutting drive at Old Trafford.

Mayor of London Sadiq Khan has risked antagonising football fans by backing calls for the Premier League to stage competitive games in America.

Team GB have hit out over the Olympic Village food, accusing the Paris hosts of serving raw meat and causing shortages which have forced them to bring in an extra chef at their own alternative restaurant.

The Paris Olympics have been hit by fresh claims of equine abuse, with show jumping medal contender Max Kuehner of Austria subject to criminal proceedings in Germany for allegedly hitting his horse's legs with a bar to make it jump higher.

EVENING STANDARD

West Ham are pushing to agree a fee with Aston Villa for striker Jhon Duran.

DAILY EXPRESS

Manchester United are reportedly eyeing Benfica's Antonio Silva as a cut-price potential alternative to Jarrad Branthwaite, according to Portuguese media.

Manchester United reportedly hold an interest in former Liverpool star Neco Williams.

Formula 1 team bosses were told to inform their drivers to be mindful of their language this week after Max Verstappen was criticised for his expletive-filled communications during the Hungarian Grand Prix.

DAILY RECORD

Sam Lammers is edging closer to a £2.7m move to Twente Enschede - in a deal which could unlock the cash for Rangers' bid for Lawrence Shankland.

Rangers captain James Tavernier is reportedly "keen" on joining up with former boss Gio van Bronckhorst at Beskitas this summer.

Sevilla want to insert an obligation for Rangers to buy Joan Jordan for a fee of up to £4m if they agree a loan deal for the midfielder to move to Ibrox, according to a report.

SCOTTISH SUN

Vaclav Cerny has given back his company car and will be left out of Wolfsburg's team photo as he finalises a move to Rangers, according to a report in Germany.

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