Chapter 49 Basic Concepts in Sports Biomechanics Tommy Boone, PhD, MPH, FASEP, EPC and Larry Birnbaum, PhD, MA, EPC   Biomechanics is the study of the structure and function of biological systems by means of the methods of “mechanics.” – which is the branch of physics involving analysis of the actions of forces.  Within “mechanics” there are two sub-fields of study: (1) statics, which is the study of systems that are in a state of constant motion either at rest (with no motion) or moving with a constant velocity; and (2) dynamics, which is the study of systems in motion in which acceleration is present, which may involve kinematics (i.e., the study of the motion of bodies with respect to time, displacement, velocity, and speed of movement either in a straight line or in a rotary direction) and kinetics (the study of the forces associated with motion, including forces causing motion and forces resulting from motion). Biomechanics is therefore not kinesiology (which is often another name for physical education).  There are numerous titles of books that are confusing, especially since the titles suggest more than the definition of biomechanics that was stated earlier.  Examples include, but are limited to, Fundamentals of Sports Biomechanics, The Mechanics of Athletics, Scientific Principles of Coaching, Biomechanic Analysis of Sport, Biomechanics of Sports Techniques, Biomechanics of Human Motion, and Mechanical Kinesiology.  BIOMECHANICAL ANALYSES In general, there are two approaches used to study mechanical aspects of human movement.  There is the quantitative approach that involves the use of numbers.  This approach helps to eliminate subjective description and relies on data from the use of different instruments.  It is a more scientific, publishable, and predictable analysis than the qualitative approach that implies that the movement is described without the use of numbers.  This approach is used a lot in coaching and during the teaching of sports skills.  Both quantitative and qualitative descriptions play important roles in the biomechanical analysis of human movement.  Biomechanical analyses can be divided into four areas. (1) noncinematographic analysis;  (2) basic cinematographic analysis; (3) intermediate cinematographic analysis; and (4) Biomechanics research. • Noncinematographic analysis is the most common analytical technique used in sports by coaches, athletes, and others.  No film or videotape is used in capturing the performance and/or component parts of the execution of the motor skill.  It requires a disciplined approach to observing and, then, analyzing skills, but does not require intricate mathematical calculations.  It does require a full understanding of biomechanical principles.  Obviously, a qualitative analysis is subject to some error in interpretation. • Basic cinematographic analysis involves the use of film or videotape for improving performance.  It does not involve any mathematical calculations.  One advantage of noncinematographic analysis is that you can see the movements in slow motion (frame by frame).  The analysis allows for seeing what actually occurred versus what you may think took place.  It is helpful in reducing the amount of guess work and, thus error in correcting motor skills since it is a qualitative analysis. • Intermediate cinematographic analysis requires some mathematical computations to enhance the analysis.  The use of film is necessary to capture the motor skill and subsequent analysis.  It is a quantitative analysis, where velocity and force (along with other data) are calculated, thus allowing for a significant reduction in guess work in analysis of component parts of a given skill.  As a result, the analysis increases the chances of teaching the skill correctly. • Biomechanics research involves highly sophisticated biomechanical equipment, such as high speed cameras, EMG for muscle involvement, force plates, transducers, computers, and much more.  The equipment allows for very accurate determination of factors that influence human performance.  It is the method for publishing in scientific journals, and usually a doctorate in biomechanics is needed.  As you might imagine, it takes a lot of time to reduce the data before treated with statistical procedures. NEWTONIAN LAWS Law of Inertia Newton’s 1st Law states that an object continues in a state of rest or of uniform motion in a straight line unless acted upon by an external force.  Inertia is Latin for idleness or laziness.  The Law of Inertia can be interpreted as everything in the universe is lazy, thus requiring a force to get it on the move (which then occurs in a straight line).  Once moving, more force is needed to slow it, stop it, or to speed it up or to change direction.  Inertia is the body’s resistance to change in movement.  It is proportional to mass, thus the mass of an object is the measure of its inertia.  Therefore, mass is the quantity of resistance to change.  It should not be confused with weight.  The weight of a person (or an object) is the measure of force with which the earth pulls on the body’s mass.  This downward gravitational force is the body’s weight directed towards the earth’s center.  Understandably so, a body’s mass and weight are directly proportional.  The more mass a body has, the greater the earth’s attraction on it, the more it will weigh.  Weight is a force; whereas, mass is not.  It has no direction.  Mass is the resistance to change (i.e., inertia).  Newton’s 2nd Law (the Law of Acceleration) When a body is acted upon by a force, its resulting acceleration is proportional to the force and inversely proportional to the mass.  Hence, with a constant mass, the greater the force, the greater the acceleration.  And, with a constant force applied, the greater the mass, the less the acceleration.  Another way of saying the same thing is: “The velocity of a moving object will remain constant unless a force acts on it.” Newton’s 3rd Law (the Law of Action and Reaction) The third principle of motion can be stated as follows:  If one body exerts a force on another body, the second body will exert an equal and opposite force on the first body.  Hence, it is sometimes referred to as the principle of action and reaction, which can be stated:  "For every force, there is an equal and opposite reaction force.  Essentially, Newton's 3rd Law is a statement that forces always exist in pairs.  For example, when we take a step forward, we press our foot against the floor.  Because of the friction between the foot and the floor, we exert a backward force on the floor.  The reaction force is the equal and opposite force exerted by the floor on our foot.  It is this force, which acts in the forward direction, that moves us in the forward direction.   PRINCIPLES RELATED TO THE LAW OF INERTIA Combining translatory and rotary motions The combined motions, if performed correctly with proper timing and sequence, will produce maximum final velocity of ‘an object’ in the desired direction of release (e.g., discus toss, bike riding, car, wheelchair). Continuity of motion  The accomplishment of the first motion represents the overcoming of a certain amount of inertia and, therefore, any hesitation prior to the next motion will result in loss of some or all of the advantage gained by the previous motion” (e.g., backward roll, pole vaulting).  Interruption of motion costs energy. Effects of momentum  More momentum can be produced with a longer implement in that the end will move faster than a shorter implement” (e.g., don’t choke up on a tennis racket or baseball bat). Transfer of momentum  Momentum develop in a body segment may be transferred to the total body, but only while the body is in contact with the supporting surface (e.g., earth, diving board).   PRINCIPLES RELATED TO THE LAW OF ACCLERATION Acceleration is proportional to the force causing it  A sprinter can increase acceleration by increasing the force that he/she applies backward and downward against the surface on which he/she is running” and, if he/she should double the force, then acceleration would double and, similarly, if he/she should keep the force constant and reduce mass, he/she would increase acceleration. Maximum acceleration and efficiency of motion  To achieve maximum acceleration, all available forces should be applied sequentially with proper timing and as directly as possible in the intended line of motion. Effects of body’s radius on angular velocity  The rate of rotation is increased as the radius of rotation is decreased (e.g., tuck head and bend knees; a shorter person will have a higher rate of rotation). Conservation of momentum in swinging movements To build or to conserve momentum in any swinging movement, the radius of rotation should be shortened on the upswing and lengthened on the downswing. Movements while unsupported  When the body is unsupported, movements may occur to aid in controlling balance, but the flight path (trajectory angle) will be unaffected by the movements. Twisting movements Are based on the transfer of momentum from part to whole, when in contact with a surface (have to initiate the twist in some way at take off).   PRINCIPLES RELATED TO THE LAW OF COUNTER FORCE Surface variation and the amount of counterforce  The counterforce is equal to the applied force when a stable surface is used.  The less stable the surface, the less will be the counterforce.  Examples include: (a) decreased friction on ice (fast skating); (b) increased friction running in the sand; and (c) quality of a trampoline bed (i.e., new vs. old, as in sagging). Direction of the counterforce  The direction of the counterforce is directly opposite that of the applied force.  The counterforce is most effective when it is perpendicular to the supporting surface.  If not perpendicular, the force is separated into two components, vertical and horizontal.  Hence, it is important to consider the trajectory angle. Counterforce in striking activities  The amount of force a striking implement imparts to an object depends upon the combined momentum of the implement and the object at the moment of impact (i.e., how is the force dissipated).  Also, it depends on the mass of the object and the implement.  Examples include baseball bat hitting a baseball or a tennis racket hitting a tennis ball. Temporarily stored counterforce  If a surface or implement used in a performance has elasticity, then an applied force produces bend or compression that represents stored force, and the stored force increases the propulsive force over what it would be if elasticity were not present.  Examples include pole vaulting (e.g., fiberglass poles bend more and store more energy than aluminum poles) and diving boards (the aluminum board vs. the wooden board). Surface contact while applying forces to external objects  In throwing, pushing, pulling, and striking activities, one or both feet should be keep in firm contact with the supporting surface until the force providing motion is complete, otherwise the maximum force is decreased.   PRINCIPLES RELATED TO FORCE General Principles of Force Total force  A total force is the sum of the forces of each body segment contributing to the act, if the forces are applied in a single direction and in proper sequence with timing. Constant application of force  A force should be constant in which a minimum amount of energy is used to overcome inertia.  To do otherwise is to waste the effort (energy) put into the activity (e.g., pushing a car or some other object). Direction of force application  All forces should be applied as directly as possible in the direction of the intended motion (e.g., running with feet pointed straight forward). Distance of force application  A body develops greater velocity as the distance over which the force is applied increases (e.g., for martial arts performer rotates first to increase the force of the kick, as does the athlete who throws the shot).   SELF-PRODUCED AND OTHER FORCES Correct muscle selection The performer must select the muscles that are most effective for the task at hand. Stability and the loss of effective force  A spotter must be stable before he/she can prevent a loss of force to the performer. Effect of the angle of application on the force produced In angular movements of body segments, the maximum effective force and velocity occur when the limb is at right angles to the direction in which the object is moved” (e.g., karate punches in which the arm straight forward, not up or down, so the arm is perpendicular to the body). Initial muscular tension  Placing muscles on stretch before contraction increases in the force of muscular contraction.   APPLICATION OF THE PRINCIPLES TO THE TENNIS SERVE Of all the skills involved in tennis, the serve is the most individual.  Beginning players simply attempt to tap the ball into the appropriate court.  The more advanced players learn to place various slices and spins on the ball as it is struck.  Although an effective serve is possible, the beginning player rarely serves with much power.  This important factor in the tennis game is most often the most difficult to learn as well as to teach or coach. The power serve, as it is often called, is a skill that requires understanding of mechanical power gained through the laws of motion and force.  The technique is essentially the same throughout all individual variations and styles.  Through careful analysis of the applicable principles of motion and force, the performer of this serve should produce the desirable results. Principles of Motion Principle – Combining translatory (linear) and rotary motion.  Effective execution of a successful performance combines translatory and rotary motions. Application.  Since the serve involves synchronized motion of body levers, rotary motion is the most essential of the two motions.  The shift of weight from the back foot to the front foot as the movement begins requires rotary motion with only limited linear motion.  As the feet shift, the racket arm is extended at the side and slightly behind the hip.  The elbow then bends and the arm abducts.  As the elbow reaches the height of the shoulder, the wrist is abducted allowing the racket head to drop to a position behind the scapula.  The elbow is held high, allowing it to lead the motion of the forward swing which follows. This back swing motion must be executed in a fluent manner with the toss of the ball from the opposite arm (ball arm).  The ball arm begins its rotary motion to propel the ball upward into the air for striking.  This arm is fully extended in front of the server as the levers of the arm act to push and lift the ball.  This action gives the ball motion of its own, curvilinear motion and momentum.  Timing and the speed of the toss must be equal to that of the back swing for proper execution of the move. No pause is experienced prior to the beginning of the forward swing.  The forward swing is begun by the racket elbow leading the upward motion, and flexion and lateral rotation of the glenoid cavity (shoulder) complete the upward move.  When the arm approaches a position above and forward of the shoulder, the forearm starts its rapid extension.  At a point where the racket arm is fully extended and the wrist is adducted, the ball is struck with the upper center strings of the racket. Principle – Continuity of motion.  When performing activities in which two or more consecutive motions contribute toward movement in the same direction, the performer should not pause between motions. Application.  Each motion of the back swing and ball toss should be done by successively moving complete body parts.  This same successive motion of body parts should be executed from the termination of the back swing to the forward swing carrying through the follow-through.  Unless one wishes to overcome inertia twice, there should be no sustained pauses or jerking in the motion.  Energy is conserved in the fluent motion of performing the serve. Principle – Effects of momentum.  When a moving object strikes another object, the greater its momentum at impact, the greater the force will be. Application.  Since momentum is the product of velocity and mass, increasing either factor will increase momentum.  In a serve it is possible to increase velocity only.  The racket may in fact be larger but is rarely significantly heavier, so mass is constant.  To increase velocity, the server can produce a harder swing by increasing muscular strength of the involved muscles and can more effectively hyperextend the back to generate more stretch of the involved muscles.  These work together to product greater velocity and a more forceful movement. Principle – Transfer of momentum.  Momentum developed in a body segment is transferred to the rest of the body only while the body is still in contact with the supporting surface. Application.  The momentum generated as the forward swing begins will pull the whole body off balance.  The racket pulled, as is the arm, into a position out of the center of gravity. Principle – Maximum acceleration and efficiency of motion.  All available forces should be applied sequentially with proper timing, and as directly in the intended line of motion as possible.  Body motions extraneous to the desired motion should be minimal. Application.  The major forces in the serve follow this essential sequence: 1.  Passive extension of the racket elbow. 2.  Arm abduction along with outward rotation of the arm. 3.  Scapular adduction and upward rotation of the glenoid cavity. 4.  Rotation of the thoracic spine. 5.  Elbow flexion of the ball arm. 6.  Elbow extension of the ball arm along with relaxation of the finger flexors. 7.  Elbow extension of the racket arm with hyperextension of the back. 8.  Adduction of the arm, inward rotation of shoulder and hyperextension of the racket elbow. 9.  Trunk flexion with hip flexion. The follow-through is a continuation of all of these.  Because of the strength and speed necessary for the serve, it must be executed in this sequence vigorously.  The ball arm is usually carried behind the server to maintain balance. Principle – Counterforces in striking activities.  The amount of force a striking implement imparts to an object depends upon the combined momentum of the implement and the object at the moment of impact.  Give in the implement reduces propulsive force. Application.  Strong muscular contractions of the involved muscles are essential for reducing the loss of force due to the give in both the racket and ball.  Grip on the racket should be firm, and the back foot must push strongly.  Tension increases on the strings of the racket may reduce loss of force as well. Principle – Direction of the counterforce.  The counterforce is directly opposite and equal to the applied force. Application.  The push of the back foot along with the strong adduction of the arm overhead produce the applied force of the swing.  The first force requires a strong push to propel the server upward and slightly outward leaving the ground.  The tendency to push too far forward reduces the advantage of the downward swing of the racket.  Full power is attained when hitting the ball at the top of the forward swing.  A broader starting stance insures more weight transfer is placed on the back foot. Principle – Temporarily stored counterforce.  If a surface, implement, or object used in a performance has elasticity, then an applied force produces bend or compression, which represents stored energy. Application.  Rackets may be strung at various tensions.  Some players prefer more tension on the strings to product more power to the serve.  A reduced tension adds energy to the striking force, but at the same time may reduce momentum of ball placement. Principle – Leverage.  By changing the amount and type of leverage, either speed (and distance) or force can be gained at the sacrifice of the other. Application.  The serve uses third class body levers.  These levers produce speed and range of motion (distance) at the expense of force.  Third class levers are especially effective in producing a fast striking force with a relatively light object.  By applying a total range of motion to each lever and utilizing great muscular force, the optimum effect can be obtained. Principles of Force Since there is a direct relationship between force and motion, many principles of force have already been discussed.  The principles not yet identified are: Principle - Total force.  The total force is the sum of the velocities of all contributing movements, if the movements are applied in a single direction, in the proper sequence, with proper timing. Application.  At the moment of contact, the racket head has a velocity approximately equal to the sum of the velocities of the contributing levers from the forward swing.  In order to maximize velocity, the forward swing should be performed in the proper sequence already discussed.  If the proper sequence is applied but timing is off, the performer will not produce the most effective serve.  Timing takes considerable practice, since the toss of the ball and the height at which the forward swing is applied requires precise motions. Principle – Duration of force application.  If a constant force is applied to a body, the body develops greater acceleration as the distance over which the force is applied increases. Application.  For maximum duration (distance) of force application, the back swing should be executed with hyperextension of the back and the racket head at the scapular level.  The hyperextension of the back allows the performer more distance for stretch of muscles necessary to perform the forward swing.  An optimum back swing and total body shift will produce the optimum duration of force. Principle – Follow-through.  Emphasis on a correct follow-through eliminates a tendency to decelerate the striking action prior to contact. Application.  During the follow-through, the racket arm descends toward the ground under the influence of gravity.  The weight then shifts from the back foot, the front foot as the back foot is thrust forward.  The ball arm is carried back to act as a counter-balance to maintain balance.  Adequate follow-through is vital to a forceful and complete serve.  Lack of follow-through increases the force applied by antagonistic muscles and reduces the force applied at the moment of ball contact.  Concentrating on the follow-through may help control the consistency of agonist muscular contractions during the forward swing. Principle – Effects of spin on the ball.  The flight of an object is influenced by the direction and amount of spin on it. Application.  We know that a spinning ball curves from an accumulation of air resistance on the forward spinning side of the ball.  The amount and direction of wind must be considered when application of the height of the toss is made.  The toss must be executed at a height approximately equal to the reach of the racket head at the peak of the forward swing. Principle – Force causing the projection.  The force causing the projection produces varying effects depending upon its point of application. Application.  The position of the racket head as it contacts the ball will produce the desired slice.  Off-center contact produces rotation.  To produce the desired spin, the ball will have to be hit slightly over the top and mostly on the right (right-handed player) side.  Hitting the ball on the upper right quarter segment will maximize the desired slice.  The imparted slice will cause the ball to curve in flight from the server’s right to left and away from the receiver. Final thoughts The analysis of the mechanics of the tennis serve is rather detailed; however much detail has been omitted due to length and space to do so.  The essence of the mechanics have been covered in an attempt to aid the performer eliminate common errors.  Major forces have been identified and the proper sequence and timing were emphasized. For the serve to be executed with the maximum success, a full baseball-throw arm motion is necessary.  It may be helpful for the beginner to pretend the racket handle is a baseball and attempt to “throw” the head of the racket at the ball.  It may be questionable as to whether or not a pause or hesitation is experienced between the forward swing and the back swing.  In order to avoid overcoming inertia twice, the serve should be executed without hesitation. For the teacher/coach wishing to improve the performance of a player, encouragement should be given to provide adequate and essential practice time on the serving skill.  Strengthening exercises for the arm and shoulder, which can also improve the speed and flexibility of these areas, should be encouraged.  To attain the maximum degree of power and skill, both beginning adults and children should engage in such exercises.   FORCE ABSORPTION An athlete prepares for impact (as when falling) by placing the shock absorbing joints in extension, but not locked.  The same is true when catching a baseball.  The position of the limbs provides more distance to absorb the force compared to a flexed position (shorter distance).  As contact is made, the extended joints flex due to the impact and immediately absorb the force of impact.  The force is gradually reduced by eccentric (i.e., lengthening) contraction of the (e.g., elbow) extensors (and shoulder flexors).  The force of impact is distributed over either a greater time (distance) or area of the body or both. TYPES OF MOTION When static balance has been upset, the body has been put into MOTION.  Thus, what is implied is a change of place or position involving direction and speed.  There are three major classifications of motion:  • Linear motion • Curvilinear motion • Rotary motion Linear motion (also known as translation or translatory motion).  Meaning, a person is said to move as a whole with all parts moving in the same direction.  If the path is straight, it is linear.  Linear motion is also referred to as rectilinear motion, although it has become customary to use only the word linear.  The distance moved (i.e., the linear displacement) is measured in linear measurement units, such as feet, meters, inches, centimeters, miles, etc.  Curvilinear motion (also known as translatory non-rectilinear motion) is defined as an object that moves in a curved path.  The motion has a horizontal (straight) component plus a force that pulls it inward.  Rotary (or angular) motion occurs when some point within a system is secured or restricted so that the system will rotate around this point when it receives force.  The point serves as its axis. Linear motion When we see something or someone move we know a force is responsible for the motion.  We know this because Newton’s first law of motion says that a body at rest will remain at rest unless acted upon by a force.  This is called the Law of Inertia.  The inertia of a person or thing is essentially its mass.  Inertia is resistance to movement.  The more mass (weight) a person has the less easy it is to move that person.  Another way of saying the same thing is -- the more inertia a person has the more force which will be necessary to move that person. A force may be generally defined as a push, pull or tendency to distort.  In other words, if we see movement (push or pull) we know a force is present.  The reverse is not necessarily so, however.  It is possible to have a force (tendency to distort) without any movement.  This would happen if the force were not of a magnitude sufficient to overcome the inertia of the body.  The formula for calculating force is mass times acceleration.  Acceleration is defined as a change in velocity.  Velocity is the rate (speed) at which a body might move per a specific unit of time (such as feet per second or miles per hour).  Therefore, when we see a body change its velocity, we know a force has acted on it.  In the simplest sense, this could mean that a body was standing still and then moved.  It could also mean that a body was moving and then changed its velocity (as in speeding up or slowing down).  If this were the case, again, we would know by Newton’s first law that a force is present.  We know this because Newton’s first law states that a body in motion will continue in motion in the same direction at the same velocity unless acted upon by some force.  This introduces another possibility, that is, a body could move in one direction and then change direction.  When this happens, we know that a force caused the change in direction. Once a body has been put in motion, it has momentum.  How much momentum it has is determined by how fast it is moving and how much mass it has (by formula, Momentum = Mass x Velocity).  This would imply that while a force acted on the body to move it (a force sufficient to overcome its inertia), the force is no longer acting on it.  Since Newton’s Law of Inertia says that the body will continue to move unless acted on by another force we would expect to observe the momentum of that body continue unless resistance forces (such as gravity, friction, or air resistance) slow it to a stop. It should be obvious that it is going to take more force to move a large mass.  Ten pounds is twice as much as five pounds.  It will take twice as much force to move 10 pounds as it will to move five pounds.  When enough force is applied to move either 10 pounds or five pounds and they were both given the same speed of movement (velocity), the 10-pound weight would have twice as much momentum.  Remember that momentum is not just velocity.  While momentum is movement, it is made up of both velocity and mass.  For example, it would take more effort (force) on your part to catch the 10-pound weight (twice as much effort) as it would for the five-pound weight if both traveling at the same speed (velocity). The effect of gravity on the body Gravity is a force because it tends to accelerate a body.  Gravity is a phenomenon that exists on earth.  It is a force that attracts everything in the earth’s atmosphere to the center of the earth.  It is as if the center of the earth is a magnet that draws everything with mass towards it.  The attraction is greatest the closer a body is to the center of the earth.  For example, the gravitational attraction is greater for someone in Wisconsin than it would be for the same person in the mountains of Colorado. Gravity is what causes our weight.  How much mass we have and what that mass is made of will determine the attraction of our bodies towards the center of the earth.  When we place a scale between the center of the earth and us, the scale will measure that attraction.  A person with more mass will be heavier. It is important to understand that the effect of gravity is very close to being a constant.  That is, the force of gravity will accelerate any body at the same rate (e.g., 32 feet per second per second).  That means that as long as a body is free to fall it will accelerate at a rate of 32 feet per second every second.  A body dropped from a plane will have a velocity of 32 feet per second at the end of one second, 64 feet per second at the end of the second second, 96 feet per second at the end of the third second and so on. Although, in most sports situations, we will not reach these velocities, the principle remains the same – as a body is allowed to fall, it will accelerate at a rate of 32 feet per second every second regardless of its weight.  Air resistance becomes a retardant force when the shape of the body is such that it will present more surface area to the air below it.  A skydiver will slow down in the air as he/she becomes spread eagle, and will speed up if he/she drops feet or head first.  The effect of air resistance is very dependent also on the speed of the object.  It becomes more of a factor when a body is going a great speed.  For all practical purposes it does not affect athletes in sports such as various gymnastics activities. While it is important to understand that a light body will fall at the same rate as a heavy body, the momentum of each will be different.  Taking the two weights we used before (five and ten pounds) and dropping them from the same height will give us the example that we need.  Both weights will fall at the same rate.  They would both hit the ground at the same time.  However, the ten-pound weight will have twice as much momentum or twice as much impact as it hits the ground.  It would take twice as much resistive force to stop the ten-pound weight at any time in the air. Application of these linear forces to the body All of this knowledge is necessary to understand how to get force, how to direct it, and some of the problems of moving and/or stopping bodies that have more mass.  Muscles are responsible for generating much of the force to move the body and to redirect it once it is moving.  How well it moves depends on how much force can be generated (strength and/or power) and how much inertia (body weight) there is to overcome.  Athletes need to know what the objective of each skill is and how to position the body to direct the necessary forces appropriately.  When gravity is used as the prime mover of the body, athletes must come to an understanding of its positive and negative effects.  In so doing, they are able to adjust body parts and/or position to, for example, spot gymnast during the learning phase of the gymnastic skills.  Similarly, mats should be arranged in anticipation of landing areas based the coach’s ability to control the momentum of the gymnast. Angular movement Angular movement is rotational movement.  When something rotates, it always turns about an axis.  The axis may be real as in the hinge of a door, the center of a turnstile, the axle of a wheel, or a horizontal bar.  It may be imaginary, as a body rotates in the air, free of support.  In this case, the axis of rotation is the exact center of gravity of the body.  This is the point at which all of the weight of the individual is centered (i.e., the exact middle of the body).  That middle or center changes every time the body changes shape.  If the arms are raised overhead, weight is moved away from the original center of the body and now the center has moved in that direction.  When a body is in the air rotating, it always rotates around its exact center no matter where that center is located.  Angular motion is described by degrees through which something moves. The concepts of angular motion are similar to linear motion, but the terms change in order to specifically identify an association with rotation.  It still takes a force to overcome inertia in order to produce momentum.  The force of rotation is called torque.  Torque is required in order to rotate a body.  Instead of having to overcome simple inertia (weight or mass), we must now overcome angular inertia.  Not only does mass resist movement but also, when you are trying to turn a body, the length of the body has an effect on how easy it is to turn.  The longer a body is, the more difficult it becomes to turn the body.  So now there are two factors that constitute the angular inertia of a body–the mass and the length of the body.  There will be more angular inertia (more resistance to torque or angular force) the more mass the body contains and the longer it is when the force is applied. Once a force (torque) of sufficient magnitude (enough to overcome the angular inertia) is applied to a body, angular momentum will be produced.  The total amount of angular momentum will depend on the angular inertia (i.e., how much mass and how long the body is) and the speed (angular velocity) the body is turning.  It is important to know how torque is created.  Generally it is a combination of two forces (in physics terms – a force couple).  For example, it is possible to cause rotation of a body by what we might call a “tripping effect.”  Much the same as one might trip over something when walking (the effect of which would be to rotate forward and possibly fall on the face) and thereby fall into or “trip” into a forward roll.  A gymnast does this by first running forward (creating horizontal momentum).  By bringing the feet together (hurdling) and planting the feet on a vaulting board or mat the feet stop by virtue of a restraining force (friction).  With the combination of horizontal momentum and stopping of the feet, the gymnast creates a force couple.  During the time the feet are in contact with the board or mat, the body is free only to rotate.  The axis of rotation becomes the point at which the feet are in contact with the board or mat.  If the feet remain in contact, the body would literally fall flat on its face.  What usually happens is that the person pushes with the legs downward on the takeoff surface with enough force to raise the body go into the air.  When it goes in the air it will (depending on the magnitude of all these forces) continue to move forward as a result of the run, move upward as a result of the push down, and rotate as a result of the “tripping effect” created by stopping the feet and having the body move forward. It is also possible to rotate the body by applying what is called an eccentric force (i.e., a force that is not directed through the center of gravity of a body).  For example, when we walk through a revolving door, we direct our push close to a right angle (90°) to the door.  We do not push on the end of the door in the direction of the axis of rotation that would also be the center of weight.  If we think of a circle with the axis of rotation of the door in the center, then the door would become the radius of the circle.  Rather than apply a force in the direction of the radius, it applied at a right angle to the radius (tangent to the circle).  Another example might be to balance a stick (not on end) in the middle of your finger.  If you now push up and send the stick into the air it should not rotate (not if your finger was directly below its center of weight – the condition necessary to balance).  However, if you place your finger away from the center of gravity and conduct the same experiment you will find that the stick will not only go up but will also rotate.  The further away from the center that you place your finger the more rotational and less vertical effect you will have on the stick.  We use this method of producing rotation by having the body lean in one direction or another while a force is not directed through the exact center of gravity of the body.  As a result, the force, in the case of a gymnast or a diver leaving the springboard, will initiate a flipping or turning effect.  The more lean there is the more flipping and the less vertical effect there will be. It is important to realize that all the angular momentum one creates is created while the body is still in contact with the ground or the apparatus, in other words, at the time of the take off.  This angular momentum is a product of the angular inertia (mass and the length of the body) and the angular velocity created.  Once in the air, it is impossible to create any more angular momentum. However, when a person is in the air, free of support and rotating, it is possible to change the variables that make up angular momentum.  Remember that Angular Momentum = Angular Inertia x Angular Velocity.  What we can easily see while a person is multiple somersaulting from a great height is a change in angular velocity.  What we sometimes do not perceive is a concurrent (at the same time) change in angular inertia.  While it is impossible to change the mass of the body while it is in the air, we can change the shape of the body at will.  When we extend the body (stretched body position) it is the longest it can possibly be relative to forward, backward or sideward rotation.  If the body were rotating forward then we would have the most angular inertia in a stretched body position and the least in a tucked position.  While in the air rotating around a horizontal axis (somersaulting), we could increase our angular inertia (lengthen our body) in order to slow the angular velocity, or we could decrease our angular inertia (shorten our body) in order to speed up our angular velocity.  One factor will decrease by the same amount that the other will increase so that the total angular momentum will never change. Pendulum swing  When on the apparatus we can develop angular momentum in a fashion similar to the “tripping effect.”  The major difference is that instead of a horizontal force initiating movement, a vertical force is responsible.  That vertical force is gravity.  It acts the same on all bodies regardless of size or weight.  By virtue of a downward force (gravity) and fixing the hands or some other part of the body on the apparatus, we can create a force couple.  Because the hands or other part of the body become fixed that becomes an axis about which the rest of the body (which is free to move) will rotate. We create what we call a pendulum swing.  It is possible to swing back and forth continuing to build a bigger swing or it is possible to rotate completely around a piece of apparatus.  In either case, we are rotating during this time.  We have angular momentum.  In order to take the greatest advantage of gravity we lengthen our bodies on the down swing.  This allows the center of gravity to fall a greater distance which will give it a greater velocity at the bottom.  We must decide whether the individual has the strength to maintain the fixed contact with the apparatus.  In other words, because of an increase in angular momentum as a result of an increase in angular inertia (either because of large mass or increased length of body), the body will need an increased ability to control the increase in angular momentum.  In order to reduce the inertia at any time, but in particular, on the up swing, we shorten the body the same as we would in the air.  This will increase our angular velocity and help us achieve a complete revolution if desired.  By utilizing the same principles which governed learning to swing on the playground swings when we were youngsters, we can learn to “swing” our bodies on gymnastics apparatus.  Theoretically, a person could continue a pedulum swing indefinitely without any more effort at the level they started out.  However, friction would continuously reduce the height of the swing until the person came to a stop.  Air resistance might also be a negative factor.  What is it then which causes the person to be able to swing higher?  Since the only force that is available is the effect of gravity, the objective is try to put the body at a higher level in order that gravity has a longer time to act.  In this way the body will have a greater velocity at the bottom of the swing (which is, theoretically, the greatest velocity point during the entire arc) and will rise to a higher point on the up swing.  The only way this can be done is to reduce the angular inertia so that the angular velocity is increased.  The increase in angular velocity will result in a higher peak of up swing each consecutive time until it is possible that a body will attempt to make a complete revolution (something virtually impossible on a playground swing because the chains are not rigid and would collapse after rising beyond a horizontal position).  Since the angular inertia of the pendulum consists of its mass (weight) and its length and, since we can do nothing practical to reduce the body weight itself we have to work with the length of the pendulum.  We reduce the angular inertia by shortening the radius of rotation (bring the body closer to the axis of rotation) on the up swing.  By the same principle then, in order to maximize the effect of gravity on the down swing, we should do just the opposite, i.e., lengthen the radius of rotation by moving the body weight further away from the axis of rotation. When learning any skill involving swing we should first be concerned with developing the skill pattern with the least amount of swing possible.  The appropriate changes of shape of the body and the correct timing of those changes of shape should be learned first.  As the essential characteristics of the skill are learned, more force can be added to the skill by moving the center of weight further away from the axis of rotation on the down swing.  Since this will produce more angular momentum, there should be a concern for the safety of the individual and a preliminary judgment of whether the individual is capable of maintaining their contact with the apparatus at the bottom of the swing.  Every skill involving swings becomes a process of learning the basic movements with a minimum of swing and then adding swing in order to increase the amplitude of the skill keeping in mind that the more the body is lengthened on the down swing the greater will be the total momentum of the body at the bottom of the swing.   Selected References Dyson, G.H.G. (1962). The Mechanics of Athletics. St. Paul's House, Warwick Lane, London EC4: University of London Press Ltd. Grabiner, M.D. (1993). Current Issues in Biomechanics. Champaign, IL: Human Kinetics Publishers. Hall, S.J. (1999). Basic Biomechanics. Dubuque, IA: WCB McGraw-Hill. Hay, J.G. (1985). The Biomechanics of Sports Techniques. Englewood Cliffs, NJ: Prentice-Hall, Inc. LeVeau, B. (1977). Williams and Lissner: Biomechanics of Human Motion. Philadelphia, PA: W.B. Saunders Company. Northrip, J.W., Logan, G.A., and McKinney, W.C. (1974). Introduction to Biomechanic Analysis of Sport. Dubuque, Iowa: Wm. C. Brown Company Publishers. Simonian, C. (1981). Fundamentals of Sports Biomechanics. Englewood Cliffs, NJ: Prentice-Hall, Inc. Williams, M. and Lissner, H.R. (1962). Biomechanics of Human Motion. Philadelphia, PA: W.B. Saunders Company.