Acceleration

Without acceleration, there is little to no effect rendered by a spear thrust, a bullet or a closed fist. In all martial arts, speed of technique can determine whether your technique hits with critical impact, misses, or is countered by the opposition.

Acceleration is defined as the change in velocity over the time interval during which the action takes place.  Therefore, a=v/t ( a =accleration, v =velocity, t =time ).  This is the rate at which the velocity changes.  Acceleration is measured in m/s^2 or m/ s/s ( m =meter, s =second).

Acceleration lends to the successful execution of a devastating elbow strike or to the snappiness of a quickly applied joint lock technique such as an arm bar or choke.  Whether you are striking to make contact or attempting to apply an instantaneous joint manipulation or lock, you must appreciate acceleration.  Acceleration, if honed by practice for control, can become a great equalizer if not an overpowering element of hand-to-hand combat over a stronger, but slower foe.

Force

A force is an agent that results in the acceleration or deformation of an object.  This agent is evident since you must accelerate your hands, head, elbows, knees and feet in order to strike targets on the opponent's body for a reason, namely to create enough injury that you disable the foe.

Force is determined by using Newton's Second Law of Motion which states that the acceleration of a body is directly proportional to the net force and indirectly proportional to the mass.  This means that in order to move a bowling ball, for example, it will take a greater force to accelerate it than to accelerate, say, a golf ball.  Also if you place the same amount of force that you used to accelerate the bowling ball on the golf ball, the golf ball will reach a much greater velocity than will the bowling ball.  The opposite is also true. If you place the same amount of force on the bowling ball that you did to accelerate the golf ball, the bowling ball will not reach as great a velocity as did the golf ball.

The formula used to calculate force is F=ma (F=force, m=mass, a=acceleration) and is expressed in newtons (N).  A newton is the amount of force that causes a mass of one kilogram to accelerate at a rate of one meter per second squared.  If an object has a net force exerted on it, it will accelerate. Force and acceleration both have direction and size.  This has greater implications than can be expressed in this type of article.  The fact remains however that these principles provide for the basis and resolution of muscular contractions that result in the internal tension and subsequent movement of the skeletal system.  I will not cover angular and stabilizing vectors since the purpose of this article is to dilineate the basic knowledge of physics that our predecessors lacked.

What would you do with this knowledge if you were a medieval general tasked with quickly preparing your men for armed and unarmed combat?  Whereas the Roman Legions incessantly drilled weapons movements as well as unarmed strikes, you personally may simply want to make sure that over time, your men had developed a sense of how much force was being generated by their acceleration.  You then would probably lean towards having them train in increasing their acceleration.  Then again, you could have them body train to gain muscle mass.  If you were pressed for time, which would you choose to develop in your army, acceleration or mass, to generate the highest levels of force? If you said both, you are probably correct.   

 Momentum

The momentum of an object is defined as the product of an object's mass multiplied by its velocity.  Momentum is calculated by the equation p=mv, where momentum is represented by "p".  The product of a momentum equation is labeled as kg/m/s, where kg is kilograms (1000 grams), m represents the mass of the object, and s is seconds.

In striking aspects of martial arts, momentum plays a mixture of roles.  An effective technique will require you to generate the maximum velocity allowable by time and space.

In order to find the momentum of a strike at the point of contact between two bodies of mass, assuming that the collision is inelastic, use the equation: M1V1=(M1M2)V'.  In this equation M1 is the mass of the attacking body part of the attacker, V1 is the velocity of the striking part of the body at the moment of contact; M2 is the mass of the opponent's targeted area, and V' is the velocity of the of the fist or foot of the attacker just after the collision takes place.  This equation, M1V1=(M1M2)V', is called the Law of Conservation of Momentum.  The Law states that the total momentum in a closed, isolated system does not change.  Again, the implications are boundless but remember if you increase the velocity or the mass of the striking point, you will also increase the amount of momentum transferred into the target.

                                                                                Energy

Energy also plays an important role in the physics of martial combat.  The more energy your technique possesses the more damage it will incur. 

Energy can be calculated by using the equation: KE= 1/2mv^2, where m is mass and v is velocity.  The kinetic energy is proportional to the mass of the object and is also proportional to the velocity squared.  Using this equation we see that if you double you speed, you quadruple your kinetic energy, while if you double your mass (of the arm), you only double you kinetic energy.  So by knowing this if you want to create more energy in your punch or kick,  increase your velocity and not your mass. In other words, rather than commanding your army to work out for months to gain bigger thighs or arms, develop the speed at which a kick or punch is delivered.  Have them work on each movement slowly until muscle memory etches into the brain at various timelines in the technique.  As the technique is progressively sped up, so is the fighting effectiveness of your army.