The Physics of Power Black Belt Candidate Thesis for Freedom TaeKwon-Do Schools by Patrick J. Montgomery, Ph.D. January 10, 2007

Introduction As a student of TaeKwon-Do, you may be familiar with the Theory of Power described by General Choi. The six components are as follows. 1. Mass 2. Speed 3. Reaction force 4. Concentration 5. Equilibrium 6. Breath control To learn more about these concepts, some of the underlying Physics is presented here.

Introduction  The first part gives definitions and examples of concepts, and should be accessible to all students. The last few slides contain more technical results and requires some familiarity with the use of mathematical formulas.  Further information can be found in TaeKwon-Do (The Korean Art of Self-Defence) by General Choi Hong Hi, (1999, ITF Press).  For more in depth discussion about the Physics of TaeKwon-Do, please feel free to contact the author.

Mass  The mass of an object is simply a measurement of the amount of ‘stuff’ (matter) in an object.  It is measured in kilograms, and does not depend on the shape of the object. For example, the mass of a balloon does not change when it is inflated.  An object’s mass is different than its weight. An astronaut on the moon weighs less than on earth, but has the same mass.

Mass  Mass is an important part of the Theory of Power, since an object with more mass can deliver a more powerful blow.  Which has more mass - your foot or your hand? Which do you think delivers more power?  A brick has more mass than a sponge of the same size. Which one would you rather drop on your foot?

Speed  How fast an object is moving is described by its speed.  Speed is measured as a comparison of distance to time. For example, the school zone speed limit is 30 kilometres per hour. The speed of light is 300,000 kilometres per second!  Velocity is a more specific term for speed, and includes a direction. Two birds flying at the same speed but in different directions would have different velocities.

Speed  A faster object will be able to impart more power, so speed is important.  An elastic band will only sting if it is snapped at a high speed. If you threw an elastic band like a ball, would it hurt anyone?

Momentum  Both mass and speed must be considered together to understand their relationship to power. Momentum is the amount of ‘oomph’ that an object in motion has.  More precisely, momentum is the product of mass and velocity. An object with zero speed has zero momentum.  An object’s momentum will determine how much power is available.

Momentum  As an example, imagine a basketball and a bowling ball (roughly the same size and shape.) The bowling ball is has more mass than the basketball. If both the basketball and bowling ball were dropped off of a roof, they would hit the ground with the same speed. The bowling ball would have a larger impact because of its greater momentum.  This principle is why a small rock can crack a windshield on a car travelling on the highway.

Force  A force is simply a push or pull on an object.  Forces can cause objects to move (when you kick a ball,) change direction (when you kick a ball in motion,) or stop (when you catch a ball.)  Forces can cause acceleration of an object, or changes in its velocity. For example, you feel a force pushing you back in your seat when you are in a car that is speeding up (accelerating.)  Forces can change an object’s momentum.

Reaction Force  The term reaction force has two parts to it.  The first part is the equal and opposite force from the body that the force is acted upon.  For example, when you push on a wall, the wall exerts just as much force on your hands as you do on the wall. The harder you push, the more the wall seems to ‘push back’.

Reaction Force  The second force described by reaction force is more correctly referred to as a ‘force couple’ or torque (pronounced ‘tork’).  Torque causes a pivoting or twisting motion.  A lever is a simple example – if you push down on one end, the other end is pushed up.

Reaction Force  As an experiment, try making a middle forefist punch with your left hand, while keeping your right hand behind your back. Next, make the same punch while at the same time pulling your right hand back to your right hip. Which punch has more power?  The action of pulling your hand in the opposite direction of your punch helps you rotate your body, and increases your power.

Pressure  When you exert a force on an object, this is a form of pressure.  You feel the pressure of water pushing on your ears when you dive to the bottom of a swimming pool.  This type of pressure depends on the force and the area over which it is applied. A higher pressure is achieved from concentrating a force over a small area.

Work  When you push an object across the floor, you are using your body’s energy to move an object. The concept of a force moving an object a certain distance is called work.  Work is the product of the force applied to an object and the distance the object travels. Pushing a heavy object a short distance uses the same amount of work as pushing a lighter object a further distance.  The work necessary to move an object depends on a number of factors such as shape, mass, friction, and floor slope.

Energy  The word energy can mean many different things, from the energy that you have to make your body move to the energy that heats your home.  Kinetic Energy is the energy of a moving object. It depends on both mass and velocity, and increases with both of these.  When you strike a board, you are transferring energy from your body’s muscles into the kinetic energy of your hand or foot.

Power  The last concept to be described is power. Power is the rate at which energy is transferred between objects.  For example, it takes roughly the same amount of energy to walk or run up a flight of stairs. You create more power by running up the stairs because you reach the top faster.  A faster energy transfer creates more power.

Power  To break a board, you must overcome the board’s ability to hold together. You must exert a force over a certain distance. Your attacking tool must have enough energy and exert enough pressure to do this work.

Equations  Many of the ideas discussed in the previous slides are more concisely expressed through algebraic notation. This formulation permits the concepts to be precisely related to each other.

General Choi tells us that studying the Theory of Power will help improve our level of proficiency in TaeKwon-Do and achieve more of the potential that lies within us: “Though training will certainly result in a superb level of physical fitness, it will not necessarily result in the acquisition of extraordinary stamina or superhuman strength.”