Physics and its application in martial arts need to be understood clearly. Martial artists know that martial techniques need to be executed fast and often forcefully. The meaning of “fast” is generally understood to be speed, or velocity, or acceleration, which may be wrongly understood as being synonymous. Again, their relationships in forming potential or kinetic energy, and how they all link up in creating force, are also usually not clearly understood. Hence an overview of theoretical physics is required to be understood before attempting to understand how it relates practically in the field of martial arts.

# Theoretical physics

The concepts of physics that need to be understood are of speed, velocity, acceleration, potential energy, kinetic energy, and force.

## Speed

The definition of speed is generally credited to the Italian physicist Galileo Galilei, who gave the definition that speed is the distance traveled in a unit of time.

Speed is defined as the distance traveled in a unit of time. Because speed shows only the magnitude and not the direction, it is a scalar quantity.

**s = d/t**

where,

d = distance, generally measured in metre/kilometre/miles/knots

t = time taken, generally measured in per second/minute/hour

s = speed, generally measured in m/s, or km/h, or mph

For example, a car wants to cover a distance of 20 kilometres (km) in 2 hours (h), then the speed of the car would be 20/2 km/h, or 10 km/h.

*corbettmaths video “Speed, Distance and Time”:*

### Non-varying or Constant speed

Speed that does not vary or change, is known as a non-varying or constant speed. For example, if a car wants to cover a distance of 60 kilometers in a time of 8 hours, then the speed of the car should be 60 km/ 8 hours = 7.5 km/h. So, if the car can complete 7.5 km in one hour, then in 8 hours it will complete 60 kilometers. Since the speed of the car did not change during the entire distance, this speed is known as a non-varying or constant speed. Constant speed signifies uniform motion.

### Varying or Non-constant speed

Speed that changes or varies, is known as a varying or non-constant speed. Generally, objects do not have uniform motion and do not have a constant speed. Non-uniform motion signifies varying or non-constant speed.

For example, the car had to initially start and at that instant of time, the speed is 0 km/h. But to move, the car has to change the speed. Assuming the car moves by changing the speed to 7.5 km/h. At that instant, a specific moment in time, the speed is 7.5 km/h, which can be seen in the speedometer of the car. After going some distance, the car finds another car in front of it. So, now the car has to slow down to say a speed of 5 km/h. At that instant, the speed of the car is 5 km/h. Thereafter, the traffic clears and the car attains a speed of 20 km/h. At that instant, the speed of the car is 20 km/hr. Then, with a clear road ahead, the car goes at a speed of 60 km/h. At that instant, the speed of the car is 60 km/hr. Finally, the car covers a distance of total 60 kilometers in a total of 8 hours and stops, when its speed is again 0 km/h. Thus, it can be seen that at different instances of time, the car had different speeds of 0 km/h, 7.5 km/h, 5 km/h, 20 km/h, 60 km/h and 0 km/h. Since the speed varied, it is known as varying or non-constant speed, which signifies that the car underwent non-uniform motion.

### Instantaneous speed

The speedometer of the car showed different speeds at different instances of time. Each instance of time showing its respective speed is known as its instantaneous speed at that instant. For example, the instantaneous speed of 7.5 km/h was at that instant, which is a very short time before it gets changed to 5 km/h. Again, after a short time, the speed gets changed to 20 km/h, and again after a short time, it gets changed to 60 km/h. These different speeds are the different instantaneous speeds of the car at those particular instants.

But then what is the speed of the car? How can the speed of the car be arrived at in a single value? Is the speed of the car 0 km/h, or 7.5 km/h, or 5 km/h, or 20 km/h, or 60 km/h? To find a single speed value, an average speed has to be calculated.

### Average speed

The general mathematical averaging method, where the sum total is divided by the number of units forming the summation, is not applicable to calculate the average speed. On the contrary, average speed is defined as the total distance covered divided by the total time taken. So, if the car travelled a total distance of 60 kilometers in a total of 8 hours, then the average speed of the car is 60/8 or 7.5 km/h.

Sometimes, the average speed may show a value of the instantaneous speed; however, the average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the total distance covered divided by the total time of travel), and so the average speed is often quite different from a value of instantaneous speed.

*FuseSchool – Global Education video “Average Speed | Forces & Motion | Physics | FuseSchool”:*

## Velocity

Velocity may be defined as the distance covered in a particular time along with the change in the position of the object. Velocity is defined as a measure of speed plus direction. Because velocity shows both the magnitude and the direction, it is a vector quantity.

**v = s + direction**

where,

s = speed, generally measured in metres per second (m/s)

direction = generally stated as left/right, front/back, east/west/north/south, etc.

v = velocity, generally measured in m/s direction

Speed shows only the magnitude, i.e., how fast an object is moving; whereas velocity shows the magnitude as well the direction in which the object is moving.

**For example, “6 meters per second” shows speed, while “6 meters per second east” shows velocity.**

Because speed shows only the magnitude, it is a scalar quantity, while velocity shows both magnitude and direction, and therefore it is a vector quantity.

Similar to speed, velocity may also be constant velocity, or a variable velocity, or an instantaneous velocity, or an average velocity.

*GPB Education video “What Are Speed and Velocity? | Physics in Motion”:*

If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.

## Acceleration

Acceleration is a change in velocity over time. Acceleration is a vector quantity (having both magnitude and direction). If there is a change in velocity (in either speed or direction or both), then acceleration takes place.

Acceleration is defined as final velocity minus initial velocity divided by time taken.

**a = (v – u)/t**

where,

v = final velocity, measured in metres per second

u = initial velocity, measured in metres per second

t = time taken, measured in seconds

a = acceleration, measured in metres per second squared (m/s x s)

For example, a car moving at a constant 30 kilometres per hour in a circular path has a constant speed, but it does not have a constant velocity because its direction changes. Hence, in a circular path, the car is considered to be undergoing an acceleration due to its changing directional velocities, although the speed is constant.

*Khan Academy video “Race cars with constant speed around curve | Physics | Khan Academy”:*

Similar to speed and velocity, acceleration can also be instantaneous acceleration and average acceleration. Additionally, it can also be tangential acceleration and centripetal acceleration.

## Energy

Energy has many different forms like electrical energy, chemical energy, nuclear energy, gravitational energy, electromagnetic radiation, and many more.

*EarthPen video “TYPES OF ENERGY | Physics Animation”:*

All these types of energy can be transferred from one form to another. Again, they can also be grouped under two broad classes, namely potential energy and kinetic energy.

### Potential Energy

**Potential energy is the energy that is acquired due to the position of an object.**

*Khan Academy video “Calculating gravitational potential energy | Modeling energy | High school physics | Khan Academy”:*

### Kinetic Energy

**Kinetic energy is the energy that is acquired due to the movement of an object.**

*Parth G video “Kinetic Energy EXPLAINED in 5 Levels – Beginner to Advanced (Classical Physics by Parth G)”:*

### Potential and Kinetic energy may be exchanged

For example, a runner running up a hill uses potential energy (chemical energy obtained from food) and converts it into kinetic energy (muscular energy) in order to run. While going up, the runner is experiencing resistance from air and friction from the feet touching the ground, which changes to heat energy in the body and gets dissipated via sweat. At the top of the hill, the runner gains potential energy (gravitational energy). While coming down the hill, the gravitational potential energy is used to convert into kinetic energy, but since the coming down in not without any control, so additional muscular kinetic energy is also used. Again, the air resistance and friction are experienced, which again gets dissipated in the form of sweat. Therefore, potential energy gets transformed into kinetic energy and vice-versa.

*learning junction video “Potential and kinetic energy – Law of conservation of energy – Video for kids”:*

### The sum of potential and kinetic energy remains constant

While running up the hill and coming down the hill, the runner is experiencing the exchange between potential and kinetic energies, some of which gets dissipated due to heat produced by friction and air-resistance. While going up, kinetic energy is used more and while coming down, potential energy is used more. However, if all the loss and gain, of all the energies are added up, then the total energy is always the same.

*It’s AumSum Time video “Potential and Kinetic Energy | #aumsum #kids #science #education #children”:*

### Kinetic energy can be passed from one object to another

For example, in a billiards game, a player changes the potential energy of the body into kinetic energy to move a cue stick and strike a billiards ball. The kinetic energy of the cue stick gets passed on to the struck ball, which now moves. That moving ball collides with another ball and its kinetic energy gets passed to the other ball, which begins to move. Therefore, kinetic energy can be passed from one object to another. The direction of the objects can be same, opposite, or angular.

*Alexander C video “322 – Elastic collissions of the balls”:*

### In collisions, kinetic energy can be saved or lost

Collisions can be elastic (kinetic energy is saved) and inelastic (kinetic energy is lost as heat, sound, and other forms of energy). Perfect elastic collision or perfect inelastic collision does not occur, and all collisions are approximated.

*Professor Dave Explains video “Elastic and Inelastic Collisions”:*

### In rotational motion, kinetic energy can be stored

A flywheel is used in several mechanical machines, and it shows that kinetic energy is stored in rotational motion.

*Tom Stanton video “Flywheel Battery”:*

### Kinetic energy formula

Different formulas of kinetic energy are used for different physical situations. If the speed is equal or greater than the speed of light, then the relativistic formula of kinetic energy is used. If the object is small enough to be atomic or sub-atomic, then the quantum mechanical formula of kinetic energy is used. However, for common human experiences of processes and objects, the classical mechanics formula of kinetic energy is used, which states that the kinetic energy is equal to 1/2 the product of the mass and the square of the speed.

The formula form is as follows:

**KE = 1/2 m (v x v)**

where,

KE = kinetic energy, measured in joule

m = mass, measured in kg

v = velocity (or speed), measured in m/s

**Note:** In this formula, velocity signifies only the magnitude of speed without any specific direction, as it can be in any direction, and so usually v is called as speed instead of being called as velocity.

For example, the kinetic energy of an 80 kg mass (about 180 lbs) traveling at a speed of 18 metres per second (about 40 mph, or 65 km/h) would be 12.96 kilojoule.

KE = 1/2 . 80 kg . (18 x 18) m/s = 12,960 J = 12.96 kJ

**The formula of Kinetic Energy concludes that:**

**—if m (mass) is doubled than KE (kinetic energy) is doubled.**

**—if v (speed) is doubled then KE (kinetic energy) is quadrupled.**

## Force

*Hungry SciANNtist video “What is Force? | Contact Force and Non-Contact Force | Science Lesson for Kids”:*

Force is defined as mass multiplied by acceleration.

**F = ma**

where,

m = mass, measured in kilograms (kg)

a = acceleration, measured in metres per second squared (m/s2)

F = force, measured in Newtons (N)

Therefore, the greater the mass or acceleration, the greater will be the force.

*Lectures by Walter Lewin. They will make you ♥ Physics. video “When a physics teacher knows his stuff !!”:*

## Equilibrium

A body is said to be in equilibrium when the net force acting on it is zero. Equilibrium may be neutral, stable, or unstable.

*Flipping Physics video “Stable, Unstable, and Neutral Equilibrium”:*

# Application of Physics in martial arts

The above concepts of physics are suitably incorporated in all traditional martial arts of the world. These concepts can be found in stances, techniques of attack and defense, patterns, sparring, and self-defense.

## Stances

All stances are so designed that equilibrium of the body is maintained while standing or while in motion. Stances provide balance and stability during the execution of martial techniques.

*Jesse Enkamp video “The Science of Karate Stances (Biomechanics)”:*

Earlier, we had learnt that equilibrium can be neutral, stable or unstable. A martial artist needs to have a stable equilibrium while making the opponent’s equilibrium as unstable. A stable equilibrium is created when starting from the center of gravity, the line of gravity remains in the base of support. Whereas an unstable equilibrium is created when the line of gravity moves outside the base of support. This concept can be seen in all throwing techniques, especially in Judo.

*Judovision video “JUDO TECHNIQUES: Base of support / Center of gravity explained”:*

For details on equilibrium please read this article:

Centre of gravity or mass, base of support, balance, and stability in martial arts

## Attacking techniques

Techniques of attack include punching, kicking, choking, vital point striking, and many more. All these techniques are taught in such a manner so that the physics behind them are suitably applied to derive the maximum force.

### Punching

Earlier we had learnt that energy gets transformed. We had also seen that in rotational motion, kinetic energy can be stored. These concepts are exhibited in the process of punching.

Before punching, the punching hand goes back to gain potential energy. At that same time the hips are twisted back, which also provides the hips with potential energy. Thereafter, the punching hand moves forward by converting the gained potential energy into kinetic energy. At that same time, the hips are twisted forward, which converts the potential energy into rotational energy and acceleration is gained. Again, at that same time, the other hand goes back in the opposite direction with a backward speed. These opposite motions lend stability to the upper body, while the opposite speeds increase the overall acceleration of the punching hand, which adds with the acceleration of the rotating hips, and this combined acceleration multiplies with the mass of the body to deliver the force in the punch. The following video demonstrates this method.

*Okinawa Karate Masters video “Basic Karate Punches | Okinawan Karate | Everyday Karate at Home | Ageshio Japan”:*

It is to be noted that the fist does not punch, the fist only makes contact, and the punch is delivered by the entire body; thereby, making it a powerful punch.

*FALKOFIRE video “Boxing – More Power from your Punches”*

### Kicking

Earlier we had learnt that in rotational motion, kinetic energy is stored. So, even if there is one spin like a wheel kick, or multiple spins in capoeira style, the kinetic energy in the kick will not be lost. This preservation of the kinetic energy in spite of one or more spins is shown in the following videos.

*UFC video “Every Wheel Kick Finish in UFC History”:*

*SOG MMA video “FIGHTERS DESTROY OPPONENTS IN CAPOEIRA STYLE ▶ AMAZING KICKS COMPILATION [HD] 2023”:*

Again, earlier we had learnt that in rotational motion, the speed can be the same, but the acceleration increases due to changing directions and therefore, the velocities also change with every rotation. The following video shows how with increased acceleration, the force is also increased with every subsequent spin.

*World Taekwondo video “Horizontal Spinning Kick Breaking – 720° Spinning Kick Quadruple Breaking”:’*

Earlier, we had also learnt that kinetic energy is quadrupled if the speed is doubled. This is seen in the following video.

*OFFICIALfighterMAN video “7 KICKS IN 1 SECONDS – taekwondo fastest kicks”:*

Also, earlier we had learnt that potential energy is due to the position of an object, and if the position is at a height, then the object acquires gravitational potential energy. This means that while the object comes down from the position of height, then the gravitational force is also added to the force of the object, which creates more force. This concept is incorporated in the axe kick, which is seen in many different martial arts.

*PhysicalMMA video “Human Weapon – Tae Kwon Do – Axe Kick”:*

*Fight Focus video “The CRAZIEST Skull CRACKING Axe Kicks and Up Kicks…”:*

## Defensive techniques

Techniques of defense generally include dodging and blocking.

We had learnt earlier that speed is a scalar quantity since it only has magnitude. Velocity is a vector quantity, since it has both magnitude and direction. If speed or direction or both are changed, then acceleration is created. Dodging employs all these concepts. Let us briefly examine each of them.

### Dodging employs the concept of speed

Evading the opponent’s moves requires speed, besides precision and lots of practice. The following video shows how dodging employs the scalar quantity of speed, as the direction of dodging can be in any direction. The logic behind dodging is firstly to not get hit and secondly, to preserve one’s own energy while the opponent’s energy gets expended.

*DAZN Boxing video “Canelo’s Head Movement Is On Another Level”:*

### Dodging employs the concept of velocity

The following video shows how dodging employs the vector quantity of velocity, as it has both speed and a particular direction. Note how the dodging is speedily done only in a particular direction so as to capture the blind spot of the opponent.

*AikidoPortal video “V2 – The Aikido strategy of getting into the blind spot! Hiroaki Izumi Sensei”:*

### Dodging employs acceleration

We had learnt that if velocity changes in either speed or direction or both, then acceleration is created. Perhaps the most famous example of acceleration in martial arts is the lunge in fencing. Lunges can be of many kinds, nonetheless, every one of them needs to accelerate at varying speeds or directions. Lunges can be used for attacking and defending. The following video shows how fencing martial artists accelerate to perform this technique and to dodge away from it.

*Slicer Sabre video “Oh Sanguk’s 4 Special Sabre Moves”:*

*Red Bull video “The Physics and Speed of Fencing”:*

The following video shows Bruce Lee performing a fencing attacking lunge in the very first move, where his fingers jab the eyes of the opponent.

*KAABA video “Enter The Dragon (Bruce Lee Vs O’Hara) HD”:*

### Blocking

Blocking can be meeting the opponent’s force with one’s own force, or it may be to deflect the opponent’s force with one’s own force. The following video shows some blocking techniques.

*沖縄伝統空手Okinawa Traditional Karate Channel video “Learn Shorin-ryu in 12min. | Minoru Higa’s practice #3 | 比嘉稔先生 | 小林流究道館｜初心者向け沖縄伝統空手”:*

*Karaté Bushido Officiel video “Okinawan Karate break a baseball bat in front of 10 000 spectators !”:*

Making contact via attacks or blocks are essentially collisions. We had learnt that collisions can be elastic or inelastic. In reality, no collision is perfectly elastic or inelastic and they are somewhere between. Hence an approximation is made, and therefore, they are approximate elastic or approximate inelastic collisions. In martial arts, since the opponents remain separate when they collide, it can be largely termed as an approximate elastic collision; however, sometimes they move together for a short time, as if it was an approximate inelastic collision, with some loss of kinetic energy in heat and sound. Thus, both approximations mixed in varying degrees can be seen in martial arts.

In the following videos, we can see how the martial artists sometimes are separate while sometimes they move together for a short time. Therefore, sometimes they meet force with force, and sometimes deflect force with force.

*Ronin Dave video “Yokozuna Hakuho vs Yokozuna Kakuryu – Outdoor Sumo”:*

*Rembuden Kendo Club video “17 World Kendo Championships 2018, Men’s Team Final”:*

## Patterns, Sparring, Self-Defense

Patterns are codified martial movements, while sparring can be no-contact, semi-contact, or full-contact, and self-defense techniques feature both simple and complex movements. All of them incorporate theoretical physics and show their practical applications in different ways.

*Jue’s Taekwon-Do video “2021 ITF World Championships- Men’s Final Patterns”:*

*LEAK លក្ខណ៍ video “Female Sparring 52kg Final(18-34 year)(🔵Australia vs DPRK🔴) ITF World Championship.ASTANA 2023”:*

*TKDTube video “DPRK Self-Defence Routine wins🏅 at the 2023 ITF World Championship in Kazakhstan”:*

## Conclusion

Force is mass multiplied by acceleration. To increase force, either mass, or acceleration, or both, need to be increased. The mass of a human body remains generally the same, and therefore it can be treated as a constant. So, what can be changed is only acceleration. Acceleration is final velocity minus initial velocity divided by time taken. Velocity is speed plus direction. Speed can be increased by exercises like speed drills and more. If speed is doubled then kinetic energy is quadrupled. So, in the velocity, what remains is direction.

Direction is like a ship’s rudder, without which the ship simply wanders around aimlessly. Direction combines with speed and makes it velocity, which goes to form acceleration, and which in turn, multiplies with mass and creates force.

All traditional martial arts of the world have their own fundamental movements. These movements, also known as fundamental techniques, have directions embedded in them. For example, a front kick has a frontal direction at high, mid, and low heights. Similarly, blocks have directions, punches have directions, and every other fundamental movement has a direction embedded within it. When the fundamental movements are mastered, then automatically, directions are also simultaneously mastered.

With expertise in fundamental movements, everything else like speed, velocity, acceleration, force, direction, potential and kinetic energies, serve their respective purposes and are never wasted.

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