Force

Here is the math

• v = s/t Constant or average velocity equals distance divided by time. When people talk about speed (how fast your fist or foot is moving) they are talking about this.
• M = mv Momentum equals mass times velocity. This is how hard you hit.
• a = (V2-V1)/t Acceleration is the change in velocity over time. Acceleration equals final velocity minus initial velocity divided by time.
• F = ma Force equals mass times acceleration.
• P = Fv Power equals force times the constant velocity.
• KE = 1/2m v2 Kinetic energy equals one-half of mass times velocity squared. This is a favorite of the proponents of velocity as it places much greater value to an increase in velocity than an increase in mass.    

Newton's Laws of Motion

• First Law of Motion. A body at rest tends to remain at rest and a body in motion tends to remain in motion, unless acted upon by external forces. This tendency to resist a change in state is called inertia. Since an opponent who is in motion tends to remain in motion, it is easier for a defender to use that motion in his or her favor rather than trying to stop the motion, such as pulling an opponent who is charging you. Since an opponent who is at rest tends to remain at rest, it is difficult for the opponent to avoid an attack quickly.
• Second Law of Motion. When a force acts upon a mass, the mass acquires a certain acceleration proportional to, and in the direction of, the force acting upon it, and the acceleration is inverse to the magnitude of the mass. In other words, a large, heavy person has an advantage over a small, lighter person.
• Third Law of Motion. For every action there is an equal and opposite reaction. Thus, when you punch an opponent with a certain force, an equal but opposite force is applied against you by the opponent's body. Therefore, you must have a tensed body and a firm, stable stance so you may withstand the force. Hopefully, the opponent will not be prepared and thus must absorb the full force of the punch. The third law also applies to technique execution. When one arm is pulled back quickly, an equal but opposite action occurs in the opposite arm. If that arm is executing a punch, the force will combine to increase the force of the punch.

Centripetal and Centrifugal Force

Two other forces that come into play during the practice of Taekwondo are centripetal and centrifugal force. Centripetal force is the force that draws objects into a spinning whirlpool. Centrifugal force is the force that throws objects off a spinning top. These forces come into play when using spinning kicks and releases that use a spinning motion.

Potential and Kinetic Energy 

Potential energy is energy at rest; it is stored and available for use. Kinetic energy is energy in motion; it is consumed as it is used. When throwing an opponent, you use your kinetic energy to lift the opponent off the floor against gravity. At the peak of the throw, potential energy is stored within the opponent. To complete the throw, you release the opponent and the opponent's potential energy changes to kinetic energy as gravity forces the opponent to the floor.

Force Deflection

An object in motion tends to remain in motion until acted upon by another force. An attack must be stopped, deflected, or avoided. The attack may come in either a straight line or an arc. Stopping the attack by meeting it head-on may be painful and you may not always be able to get out of its way. Therefore, the best strategy is to deflect the attack. A small force that cannot stop a large force may easily deflect the large force. Deflections should be used in a circular motion. 

An unskilled person will hurl their body, more or less uncontrolled in one direction, with their strike. They are functioning more or less like a falling rock. A skilled martial artist who understands the principles energy will not move in this manner. If one part of their body goes forward, another goes backward (Yin/Yang) and the forces are balanced. Therefore, pulling this person in the direction of their strike is difficult, because their inertia is balanced and not focused in one direction.

For greater striking force, you should strike the opponent on the same line as his/her inertia. If a strong part of your body is striking a weaker part of the opponent, there is no problem. However, if your weapon is not strong enough, relative to the target, this method will result in injury to yourself. If you meet force on a line perpendicular to it, your small force can deflect a larger force.

Reaction Force

For every action there is an equal and opposite reaction. Taekwondo makes use of this principle to develop powerful techniques.

One way reaction force is used is the way the pivot foot is used to thrust against the ground when shifting. The reaction force of this thrust is returned through the leg and hip to thrust the body forward.

Another way reaction force is used is through body rotation. Body rotation is created by anchoring one side of the body and using it as a pivot. The other side of the body is driven forward by the rear leg and hip as a reaction of the supporting leg's thrusting against the ground.

Hip snap may also generate a reaction force. In hip snap, the hip and leg motion, and the corresponding reaction force, is a short term, small scale pulse of power immediately followed by recoil in the opposite direction. Power is applied in a sharp pulse of energy of very short duration. Hip recoil also helps maintain stability.

These methods of generating reaction force are based on the fact that energy is being directed into the floor that bounces most all of the force back into the body, rather than absorbing it. Another way to generate a reaction force is when one hand performs a technique while the other hand is withdrawn in the opposite direction. The speed and scale of the movements of both hands are matched. This makes use of reaction force in two different ways. First, the pull back hand helps rotation to occur, because the force of the hand and arm being pulled back forcefully creates a forward movement on the other side of the body. Second, the pull back serves as a counter-balance for the technique being extended, so that if it misses the target, stability may be maintained.

Reaction force is also applied when actually striking a target with a technique. When a technique is finely focused, the body is so firmly connected to the ground that little or no force is accepted back into the body. If a technique quickly recoils after impact, none of the reaction force from the target can transfer back into the striking arm or leg and the impact duration is shortened, both of which increase impact force.