## Laws Of Kinetics

Linear kinetics provides precise ways to document the causes of the linear motion of all objects. The specific laws and mechanical variables a biomechanist will choose to use in analyzing the causes of linear motion often depends on the nature of the movement. When instantaneous effects are of interest, Newton's Laws of Motion are most relevant. When studying movements over intervals of time is of interest, the Impulse-Momentum Relationship is usually used. The third approach to studying the causes of motion focuses on the distance covered in the movement and uses the Work-Energy Relationship. This chapter summarizes these concepts in the context of human movement. Most importantly, we will see how these laws can be applied to human motion in the biomechanical principles of Force-Motion, Force-Time, and Coordination Continuum Principles.

NEWTON'S LAWS OF MOTION

Arguably, some of the most important discoveries of mechanics are the three laws of motion developed by the Englishman, Sir Isaac Newton. Newton is famous for many influential scientific discoveries, including developments in calculus, the Law of Universal Gravitation, and the Laws of Motion. The importance of his laws cannot be overemphasized in our context, for they are the keys to understanding how human movement occurs. The publication of these laws in his 1686 book De Philosophiae Naturalis Principia Mathematica marked one of the rare occasions of scientific breakthrough. Thousands of years of dominance of the incorrect mechanical views of the Greek philosopher Aristotle were overturned forever.

Newton's First Law and First Impressions

Newton's first law is called the Law of Inertia because it outlines a key property of matter related to motion. Newton stated that all objects have the inherent property to resist a change in their state of motion.

His first law is usually stated something like this: objects tend to stay at rest or in uniform motion unless acted upon by an unbalanced force. A player sitting and "warming the bench" has just as much inertia as a teammate of equal mass running at a constant velocity on the court. It is vitally important that kinesiology professionals recognize the effect inertia and Newton's first law have on movement technique. The linear measure of inertia (Figure 6.1) is mass and has units of kg in the SI system and slugs in the English system. This section is an initial introduction to the fascinating world of kinetics, and will demonstrate how our first impressions of how things work from casual observation are often incorrect.

Understanding kinetics, like Newton's first law, is both simple and difficult: simple because there are only a few physical laws that govern all human movement, and these laws can be easily understood and demonstrated using simple algebra, with only a few variables. The study of biome-chanics can be difficult, however, because the laws of mechanics are often counterintuitive for most people. This is because the observations of everyday life often lead to incorrect assumptions about the nature of the world and motion. Many children and adults have incorrect notions about inertia, and this view of the true nature of motion has its own "cognitive inertia," which is hard to displace. The natural state of objects in motion is to slow down, right? Wrong! The natural state of motion is to continue whatever it is doing! Newton's first law shows that objects tend to resist changes in motion, and that things only seem to naturally slow down because forces like friction and air or water resistance that tend to slow an object's motion. Most objects around us appear at rest, so isn't there something natural about being apparently motionless? The answer is yes, if the object is initially at rest! The same object in linear motion has the same natural or inertial tendency to keep moving. In short, the mass (and consequently its linear inertia) of an object is the same whether it is motionless or moving.

We also live in a world where most people take atmospheric pressure for granted. They are aware that high winds can create very large forces, but would not believe that in still air there can be hundreds of pounds of force on both sides of a house window (or a person) due to the pressure of the atmosphere all around us. The true nature of mechanics in our world often becomes more apparent under extreme conditions. The pressure of the sea of air we live in becomes real when a home explodes or implodes from a passing tornado, or a

fast-moving weather system brings a change in pressure that makes a person's injured knee ache. People interested in scuba diving need to be knowledgeable about pressure differences and the timing of these changes when they dive.

So casual observation can often lead to incorrect assumptions about the laws of mechanics. We equate forces with objects in contact or a collision between two objects. Yet we live our lives exercising our muscles against the consistent force of gravity, a force that acts at quite a distance whether we are touching the ground or not. We also tend to equate the velocity (speed and direction) of an object with the force that made it. In this chapter we will see that the forces that act on an object do not have to be acting in the direction of the resultant motion of the object (Figure 6.2). It is the skilled person that creates muscle forces to precisely combine with external forces to balance a bike or throw the ball in the correct direction.

Casual visual observation also has many examples of perceptual illusions about the physical realities of our world. Our brains work with our eyes to give us a mental image of physical objects in the world, so that most people routinely mistake this constructed mental image for the actual object. The color of objects is also an illusion based on the wavelengths of light that are reflected from an object's surface. So what about touch? The solidity of objects is also a perceptual illusion because the vast majority of the volume in atoms is "empty" space. The forces we feel when we touch things are the magnetic forces of electrons on the two surfaces repelling each other, while the material strength of an object we bend is related to its physical structure and chemical bonding. We also have a distorted perception of time and the present. We rely on light waves bouncing off objects and toward our eyes. This time delay is not a problem at all, unless we want to observe

Figure 6.2. Force and motion do not always act in the same direction. This free-body diagram of the forces and resultant force (FR) on a basketball before release illustrates how a skilled player applies a force to an object (Fh) that combines with the force of gravity (Fg) to create the desired effect. The motion of the ball will be in the direction of FR.

Figure 6.2. Force and motion do not always act in the same direction. This free-body diagram of the forces and resultant force (FR) on a basketball before release illustrates how a skilled player applies a force to an object (Fh) that combines with the force of gravity (Fg) to create the desired effect. The motion of the ball will be in the direction of FR.

very high-speed or distant objects like in astronomy. There are many other examples of our molding or construction of the nature of reality, but the important point is that there is a long history of careful scientific measurements which demonstrate that certain laws of mechanics represent the true nature of object and their motion. These laws provide a simple structure that should be used for understanding and modifying motion, rather than erroneous perceptions about the nature of things. Newton's first law is the basis for the Inertia Principle in applying biomechanics.

Interdisciplinary Issue: Body Composition

A considerable body of kinesiology research has focused on the percentage of fat and lean mass in the human body. There are metabolic, mechanical, and psychological effects of the amount and location of fat mass. in sports performance, fat mass can be both an advantage (increased inertia for a football lineman or sumo wrestler) and a disadvantage. increasing lean body mass usually benefits performance, although greater mass means increasing inertia, which could decrease agility and quickness.When coaches are asked by athletes "How much should I weigh?" they should answer carefully, focusing the athlete's attention first on healthy body composition. Then the coach can discuss with the athlete the potential risks and benefits of changes in body composition. How changes in an athlete's inertia affect their sport performance should not be evaluated without regard to broader health issues.

Newton's Second Law

Newton's second law is arguably the most important law of motion because it shows how the forces that create motion (kinetics) are linked to the motion (kinematics). The second law is called the Law of Momentum or Law of Acceleration, depending on how the mathematics is written. The most common approach is the famous F = ma. This is the law of acceleration, which describes motion (acceleration) for any instant in time. The formula correctly written is SF = m • a, and states that the acceleration an object experiences is proportional to the resultant force, is in the same direction, and is inversely proportional to the mass. The larger the unbalanced force in a particular direction, the greater the acceleration of the object in that direction. With increasing mass, the inertia of the object will decrease the acceleration if the force doesn't change.

Let's look at an example using skaters in the push-off and glide phases during ice skating (Figure 6.3). If the skaters have a mass of 59 kg and the horizontal forces are known, we can calculate the acceleration of the skater. During push-off the net horizontal force is +200 N because air resistance is negligible, so the skater's horizontal acceleration is: SF = m • a, 200 = 59a, so a = 3.4 m/s/s. The skater has a positive acceleration and would tend to speed up 3.4 m/s every second if she could maintain her push-off force this much over the air resistance. In the glide phase, the friction force is now a resistance rather than a propulsive force. During glide the skater's acceleration is -0.08 m/s/s because: SF = m • a, -5 = 59a, so a = -0.08 m/s/s.

The kinesiology professional can qualitatively break down movements with Newton's second law. Large changes in the speed or direction (acceleration) of a person means that large forces must have been applied. If an athletic contest hinges on the agility of an athlete in a crucial play, the coach should select the lightest and quickest player. An athlete with a small mass is easier to accelerate than an athlete with a larger mass, provided they can create sufficient forces relative to body mass. If a smaller player is being overpowered by a larger opponent, the coach can substitute a larger more massive player to defend against this opponent. Note that increasing force or decreasing mass are both important in creating acceleration and movement.

Newton's second law plays a critical role in quantitative biomechanics. Biome-chanists wanting to study the net forces that create human motion take acceleration and body segment mass measurements and apply F = ma. This working backward from kinematics to the resultant kinetics is called

Figure 6.3. Friction forces acting on ice skaters during push-off and gliding. Newton' Second Law of Motion applied in the horizontal direction (see text) will determine the horizontal acceleration of the skater.

inverse dynamics. Other scientists build complex computer models of biomechani-cal systems and use direct dynamics, essentially calculating the motion from the "what-if" kinetics and body configurations they input.

Newton's Third Law

Newton's third law of motion is called the Law of Reaction, because it is most often translated as: for every action there is an equal and opposite reaction. For every force exerted, there is an equal and opposite force being exerted. If a patient exerts a sideways force of +150 N on an elastic cord, there has to be -150-N reaction force of the cord on the patient's hand (Figure 6.4). The key insight that people often miss is that a force is really a mutual interaction between two bodies. It may seem strange that if you push horizontally against a wall, the wall is simultaneously pushing back toward you, but it is. This is not to say that a force on a free-body diagram should be represented by two vectors, but a person must understand that the effect of a force is not just on one object. A free body diagram is one object or mechanical system and the forces acting on it, so the double vectors in Figures 6.4 and 6.5 can sometimes be confusing because they are illustrating both objects and are not true free body diagrams. If someone ever did not seem to kiss you back, you can always take some comfort in the fact that at least in mechanical terms they did.

An important implication of the law of reaction is how reaction forces can change the direction of motion opposite to our applied force when we exert our force on objects with higher force or inertia (Figure 6.5a). During push-off in running the athlete exerts downward and backward push with the foot, which creates a ground reaction force to propel the body upward and forward. The extreme mass of the earth easily overcomes our inertia, and the ground reaction force accelerates our body in the opposite direction of force applied to the ground. Another example would be eccentric muscle actions where we use our muscles as brakes, pushing in the opposite direction to another force. The force exerted

Figure 6.4. Newton's third law states that all forces have an equal and opposite reaction forces on the other object, like in this elastic exercise. The -150-N (FA) force created by the person on the elastic cord coincides with a 150-N reaction force (FB) exerted on the person by the cord.

Figure 6.5. A major consequence of Newton's third law is that the forces we exert on an object with larger inertia often create motion in the direction opposite of those forces. In running, the downward backward push of the foot on the ground (FA) late in the stance (a) creates a ground reaction force which acts forward and upward, propelling the runner through the air. A defensive player trying to make a tackle (FT) from a poor position (b) may experience reaction forces (FR) that create eccentric muscle actions and injurious loads.

Figure 6.5. A major consequence of Newton's third law is that the forces we exert on an object with larger inertia often create motion in the direction opposite of those forces. In running, the downward backward push of the foot on the ground (FA) late in the stance (a) creates a ground reaction force which acts forward and upward, propelling the runner through the air. A defensive player trying to make a tackle (FT) from a poor position (b) may experience reaction forces (FR) that create eccentric muscle actions and injurious loads.

by the tackier in Figure 6.5b ends up being an eccentric muscle action as the inertia and ground reaction forces created by the runner are too great. Remember that when we push or pull, this force is exerted on some other object and the object pushes or pulls back on us too!

There are several kinds of force-measuring devices used in biomechanics to study how forces modify movement. Two important devices are the force platform (or force plates) and pressure sensor arrays. A force plate is a rigid platform that measures the forces and torques in all three dimensions applied to the surface of the platform (Schieb, 1987). Force plates are often mounted in a floor to measure the ground reaction forces that are equal and opposite to the forces people make against the ground (see Figure 6.5). Since the 1980s, miniaturization of sensors has allowed for rapid development of arrays of small-force sensors that allow measurement of the distribution of forces (and pressure because the area of the sensor is known) on a body. Several commercial shoe insoles with these sensors are available for studying the pressure distribution under a person's foot (see McPoil, Cornwall, & Yamada, 1995). There are many other force-measuring devices (e.g., load cell, strain gauge, isokinetic dynamometer) that help biomechanics scholars study the kinetics of movement.

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