Biomechanics of Sport and Exercise

Peter McGinnis, PhD State University of New York, College at Cortland

Human Kinetics

Contents

Preface

Acknowledgments

Part I Fundamental Biomechanical Concepts, Principles, and Terminology

Chapter 1 Why Study Biomechanics? What Is Biomechanics? 5

What Are the Goals of Exercise and Sport Biomechanics? 6

The History of Sport Biomechanics 12

The Future of Sport Biomechanics 14

Summary 14

Chapter 2 Anatomical Movement Terminology Body Segment, Bone, Joint, and Muscle Terminology 18

Spatial and Directional Terminology 24

Planes and Axes of Motion 25

Joint Actions 29

Summary 33

Chapter 3 Fundamental Concepts and Principles of Mechanics The Organization of Mechanics 40

Basic Dimensions Used in Mechanics 41

Newton's Laws 44

Summary 46

Part II External Biomechanics: External Forces and Their Effects on the Body and Its Movement

Chapter 4 Forces: Maintaining Equilibrium or Changing Motion What Are Forces? 50

Classifying Forces 51

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CONTENTS

Friction 52

Addition of Forces: Force Composition 57

Resolution of Forces 62

Static Equilibrium 67

Summary 72

Chapter 5 Linear Kinematics: Describing Objects in Linear Motion 75

Motion 76

Linear Kinematics 78

Summary 93

Chapter 6 Linear Kinetics: Explaining the Causes of Linear Motion 95

Law of Inertia 96

Law of Acceleration 100

Impulse and Momentum 105

Law of Action-Reaction 109

Summary 110

Chapter 7 Work, Power, and Energy: Explaining the Causes

of Motion Without Newton

Work 114

. Energy 117

The Work-Energy Relationship 119

Power 123

Summary 125

Chapter 8 Torques and Moments of Force: Maintaining Equilibrium

113

or Changing Angular Motion 127

What Are Torques? 128

Forces and Torques in Equilibrium 136

What Is Center of Gravity? 140

Summary 153

Chapter 9 Angular Kinematics: Describing Objects in Angular Motion 157

Angular Position and Displacement 158

Angular and Linear Displacement 161

Angular Velocity 163

Angular and Linear Velocity 163

Angular Acceleration 166

Angular and Linear Ac<;:eleration 166

Summary 167

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Chapter 10 Angular Kinetics: Explaining the Causes of Angular Motion 171 Angular Inertia 172

Angular Momentum 178

Angular Interpretation of Newton's First Law of Motion 180

Angular Interpretation of Newton's Second Law of Motion 183

Angular Impulse and Angular Momentum 184

Angular Interpretation of Newton's Third Law of Motion 185 Summary 186

Chapter 11 Fluid Mechanics: The Effects of Water and Air Buoyant Force: Force Due to Immersion 192

Dynamic Fluid Force: Force Due to Relative Motion 196 Summary 207

Part III Internal Biomechanics: Internal Forces and Their Effects on the Body and Its Movement

Chapter 12 Mechanics of Biological Materials: Stresses and Strains

191

211

on the Body 213 Stress 214

Strain 225

Mechanical Properties of Materials: The Stress-Strain Relationship 227 Mechanical Properties of the Musculoskeletal System 230 Summary 235

Chapter 13 The Skeletal System: The Rigid Framework of the Body 239 Bones 241

Joints 244

Summary 251

Chapter 14 The Muscular System: The Motors of the Body The Structure of Skeletal Muscle 256 Muscle Action 260

Muscle Contraction Force 265 Summary 276

255

Chapter 15 The Nervous System: Control of the Musculoskeletal System 279 The Nervous System and the Neuron 280 The Motor Unit 282

Receptors and Reflexes 284 Summary 288

I

Part IV Applying Biomechanical Principles 291

Chapter 16 Qualitative Biomechanical Analysis to Improve Technique 293

Types of Biomechanical Analysis 294

Qualitative Biomechanical Analysis to Improve Technique 295

Example Analyses 306

Summary 321

Chapter 17 Qualitative Biomechanical Analysis to Improve Training 323

Biomechanics and Training 324

Qualitative Anatomical Analysis Method 325

Example Analyses 329

Summary .342

Chapter 18 Qualitative Biomechanical Analysis to Understand Injury Development 8teven T. McCaw

Mechanical Stress and Injury 348

Tissue Response to Stress 350

Mechanism of Overuse Injury 353

Individual Differences in Tissue Threshold 354

Intrinsic and Extrinsic Factors Affecting Injury 354

Running 358

Summary 367

Appendix A Trigonometric Functions

Appendix B Answers to Selected Review Questions

Glossary

References and Suggested Readings

Index

About the Author

347

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379

385

395

399 406

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Index A abdomen 18-19 abduction 30,32-35 absolute angular position 159, 167 acceleration 44,90-93,100-105,166-167,207 activity, effect of 230-231,352-353 adduction 30,32-35 adductor longus muscle 22 age, effect of 230-231 agonist muscles 262 airfoils 204-205 anatomical analysis. See qualitative anatomical analysis anatomical axes 26-29 anatomical planes 25-29 anatomical position 24 angles 158-159,161 angular acceleration 166-167,328-329,334,337,342 angular displacement 158-163,169 angular impulse 184-185,188 angular inertia 172-178,186 angular kinetics 171-188 angular momentum 178-185

angular impulse and 184-185 human body and 179-180 Newton's laws and 180-187 overview 186-188 rigid body 178-179

angular motion 77 angular position 159,167 angular velocity 163-166,181-182,187 anisotropic materials 230 ankle 19-20,30-32,250,330-339 antagonist muscles 263 anterior, definition of 24 anteroposterior (AP) axis 26-27,30-33,35 aponeuroses 257 Archimedes 194 arm curls 134-135,138-139 arms 18-19. See also elbow articular capsule 247 articular cartilage 232-233,247-249,251 autonomic nervous system 281 average acceleration 90-91 average angular velocity 163 average speed 85-89

average velocity 88-89 avulsion fracture 231 axes, anatomical 26-29,174-175 axis ofrotation 165,174-175

B balance 286-287 ball-and-socket joints 246-247 balls

action-reaction and 110 as projectiles 97-98,100-101,208 spin on 206,315-316

baseball 13,306-310 base of support 148-154 bench presses 116,326-329 bending loads 220-223,225,235 Bernoulli's principle 204-206 biceps brachii muscle 19,22,134-135,262-264 biceps femoris muscle 23-24 . biomechanical analysis 293-321. See also qualitative

anatomical analysis evaluation of performance 304-305 fastball pitch 306-310 football punt 331-335 forehand drive in tennis 310-316 ideal technique 295-300 identifying goals 296-297 instructing performer 305-306 observation of performance 300-304 qualitative 294-295 quantitative 294-295 sprint running 316-321,334-339 technique improvement 295-306 training and 324-325 vertical jump 330-331

biomechanics 3-14 definition 5-6 friction and 56-57 future of 14 goals of 6-12 history of 12-14

body fat 195 bones

anatomy and classification 241-243 elastic modulus 231 growth and development 243-245

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bones (continued) loads on 216-218,220,222-223,230-232,235-236 long 242-245,260 marrow 242 ove;rview 240 surface irregularities 242-243 tendon attachment 259 terminology 18-19

brittleness 229-230 buoyant force 192-196,207 bursa 259

C cancellous (trabecular or spongy) bone 231,241 cardinal plane 25-26 carpals 18-20 Cartesian coordinate system 79-81, 82 cartilage 232-233,242-249,251 cartilaginous joints 245-246 cartwheel axis (anteroposterior axis) 26-27,30-33,35 catching technique 108 center of gravity

definition 140 in free-body diagrams 67-68 in human body 143-145 mathematical determination 140-143 movement and 145-147,151-153,299 stability and 147-154

center of pressure 206,359-360 central nervous system 280-282. See also nervous system centric force 128-129 centripetalforce 166-169 children, bones in 243-244 circumduction 33 clavicle 19-21 clockwise 160 colinear forces 57-59 collagen 230,232-234,236,259 combined loads 224-225,235 compact bone 231 compression 51,217-218,220,223,235,349-350 concentric contractions 260-262,273-274,276,327 concurrent forces 59-62 condyle 242 connective tissue 230-231 conservation of angular momentum 182 conservation of mechanical energy 122-123 contact forces 52 cortical bone 231-232,241 cosine function 65-66 counterclockwise 160 creep 232-234 cross-country skiing 8, 10-11, 56-57 cross-training 364 Cureton, Thomas 13 curvilinear translation 76-77

D dancing, angular momentum 185 deceleration 91 deep, definition of 24 deformation 40,216-217,220,223,225-226,233 deltoid muscle 19,22

INDEX

density 194-196,200 depression 33,35 Descartes, Rene 79 diagonal planes 29,33 diaphYSis 243 discus throwing 115,119-120,185 displacement 81-85,93,97,115-116,158-163,169 distal, definition of 24 distance traveled 80-81,83,85. See also displacement diving, moments of inertia 175-176 dorsiflexion 30-31,35 downward rotation 33,35 drafting 202, 296 drag force 197-202,208 ductility 229-230 dynamic fluid force 196-208. See also fluid mechanics dynamic friction 53-56 dynamics 41, 76, 96, 326

E eccentric contraction 261-263,273-274,277,286,327 eccentric force 128-129 effective radius 165 elastic behavior 227-228,231,233 elastic cartilage 232 elastin 230,233 elbow 19-21,30-31,250-251,338,343 elevation 33,35 ellipSOidal joints 246 endolymph 286 endomysium 257, 259 epicondyle 242

c epimysium 257, 259 epiphyseal cartilage 242-244 epiphysis 243 equipment 8-9, 12, 272. See also running, shoes Erasquin, Felix 7 erector spinae muscle group 24 eversion 30,32,35 exercise machines 272 extension 30-31, 35 external forces 52. See also forces external oblique muscle 22,24 external rotation 33-35 exteroceptors 284,287-288

F failure strength 229,235-236 fascicle 257, 259 fastball pitch 306-310 fatigue, muscle 275 femur 19-21,222-225,244 Fenn, Wallace 13 fibrous cartilage 232 fibrous joints 245-246 fibula 19-21 figure skating 10-11,67-68,182 fingers 19, 22-23 flexibility exercises 286 flexion 30-31,35 fluid friction 52-53 fluid mechanics 191-208

buoyancy 192-196

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center of pressure 206 drag force 197-202 lift force 202-206 overview 40 relative velocity 196-197,202

foot 18-19,223,358-362,365 football punt 331-335 force couples 128 forces. See also Newton's laws of motion

addition of 57-62 buoyant 192-196,207 centric 128-129 centripetal 166-169 colinear 57-59 compressive 51, 349-350 concurrent 59-62 contact 52 definition of 43,50 drag 197-202,208 dynamic fluid 196-208 eccentric 128-129 graphical determination of 63-64 gravitational 45-46,52,59 impact 108-109,328-329,334,337 injury and 348,350 lift 202-206,208 moment of. See torque in muscles 138-139,273-274 net 57,66-67, 106 normal 53-54 reaction 68-71,98,103-104,109-110,359-361 resultant 57-62 static equilibrium 67-72 tensile 51,266-274,350 torque and 136-140 trigonometric determination of 64-67 types of 51 zero net 98-100

forearm 18-19 forehand drive in tennis 310-316 form drag 199-202 Fosblll"Yr Dick 7, 9 fossa 242 fovea 242 free-body diagrams 67-71 friction 52-57 frontal plane 25-27,35 frontal-sagittal (longitudinal) axis 26-27,29,33,35 frontal (transverse) axis 26-27,30,34-35

G gastrocnemius muscle 23-24,263 general motion 77-78 gliding joints 245 gluteus maximus muscle 19,23 gluteus medius muscle 19,23 golf 164-165,178-179,206 Golgi tendon organ 286,289 gracilis muscle 22 gravitation 45-46,52,59,101,118 groin muscle 24 gymnastics 6,12,59-61,182,185

H hammer throwing 167-168 hamstring muscle 270-272 hand 18-19 head 18-19 heel 350 Held, Dick 8-9 Held, Frank ''Bud'' 8-9 high jumping 3,7-9,144,298-300,302-304 Hill, Archibald V. 13 hinge jOints 245,248 hip

in football punt 331-333,335 in javelin throwing 338,341,344-345 joint movement 30-34, 246 overview 19-21 in sprint running 338-339 in vertical jump 330

horizontal motion 96-98,101-102. See also displacement hormones, bones and 244 human body. See also qualitative anatomical analysis

angular momentum 179-181 axes 26-29,174-175 buoyancy 195-196 center of gravity 143-145 mechanical properties 230-235 moments of inertia 175-176 response to stress 350-353

humerus 18,20-21,216-218 hurdling 182-183 hyaline cartilage 232 hyperextension 30-31,35

I ice hockey 296-297 ice skating 10-11,67-68,182 impact force 108-109,328-329,334,337 impulse 105-109,184-185,187-188 impulse-momentum equation 105-108,110 impulsive load 360 inertia 42-44,96-100,172-179,186,188 inferior, definition of 24 injury 347-367

biomechanics and 11-12,235,304 cross-training and 364 factors affecting 354-358 individual differences and 354, 356 loading patterns and 359-360 mechanical stress and 348-351 overuse 352-353,358-367 psychological considerations 366-367 traumatic 353

instantaneous acceleration 91 instantaneous angular velocity 163 instantaneous speed 88 instantaneous velocity 89,318 internal forces 51 internal rotation 33-35 International Amateur Athletic Federation (lAAF) 7-9 interneurons 282 interoceptors 284 inverse dynamic analysis 326

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inversion 30,32,35 iron cross 10-11 isometric activity 273-274,276-277,327 isotropic materials 230

J javelin throwing 7-8,206-207,338-342 Johnson, Ben 86-87 Johnson, WaIter 13 joints. See also specific joint

analysis of motions 29-35,326-329,330-332 angular acceleration 328-329,334,337,342 cavities 248-249,294 classification 244-247 flexibility 249-251 javelin throw and 338 range of motion 249-250,252,329,334-335,337-339,

342 stability 248-252 terminology 18-19

joules 115-116 jumping

K

anatomical analysis 330-331 center of gravity 145-147 high jump 3,7-9,144,298-300,302-304 landing techniques 108-109 long jump 301-302 momentum 106-108 prestretch and 274

kinesiology 12-14 kinetic energy 117-118 kinetics 41,96 knee

in football punt 331-333,335 injuries 350 joint movement 30-31,249 overview 19-21 running and 361-362, 365-366 in sprint running 334-335,337,339 tensile loading 250 in vertical jump 330

Koch, Bill 8

L laminar flow 199-200,202 lateral, definition of 24 lateral flexion 30,32-33,35 lateral (transverse) axis 26-27,34-35 latissimus dorsi muscle 23-24 legs 18-19,136 length 42-43 Lewis, Carl 86-87 lift force 202-206,208 ligaments 231-234,249-251 linear momentum 105, 187 linear strain 225-226 load

bending 220-223,225,235 on bones 216-218,220,222-223,230-236 combined 224-225,235 impulsive 360

INDEX

injury and 359-360 mechanical 219-224 during running 358-362 shear 219 strength increase from 230-231 torsion 223-224 uniaxial 219,235

loading rate 231-232 longitudinal axis 26-27,29,33,35 longitudinal fibers 261,266-270,276 long jump 301-302

M

Magnus effect 205-207 Marey, Etienne Jules 13 mass 42-43,364-365. See also weight mechanics 39-46. See also biomechanical analysis;

biomechanics medial, definition of 24 mediolateral (transverse) axis 26-27,30,34-35 men, center of gravity 143 metacarpals 18,20 metatarsals 19-20 modulus of elasticity 228,233 moment arm 131,134-135,150 moment of force. See torque moment of inertia 172-179,188 momentum 105-110,187. See also angular momentum motion 76-78 motor neurons 282-286 movement, center of gravity and 151-153 muscles 255-277

contractions concentric 260-263 eccentric 261-263 in football punt 335 in javelin throwing 338-345 mechanics of 264 muscle length and 268-271

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qualitative anatomical analysis of 327-328,333-334 recruitment of 284 in sprint running 334-337, 339 types of 260-262 velocity of 271-274

effect of inactivity 352-353 fibers

contractions and 265 fatigue and 275 longitudinal 261,266-270,276 nervous system and 282-283 pennate 261,266-270,276 structure of 257-261 Typel/ll 275

force and 138-139,265-276,283 length of 268-271 line of pull 260 maximum tension in 270,284 mechanical properties of 234-236 moment arms in 162-163 nervous system and 282-283 overview 19-24 power output and velocity 271-274,276-277

qualitative analysis of 325-329 range of motion and 252 roles of 262-264 single- vs. multiple-joint 270-271 spindles '285-286 structure of 256-260,265 torque in 132-134,186,262-263,276 types of 256

myofibrils 257-259,265 myofilaments 257-258,265

N neck 18-19,31-34,242 nervous system 279-289

exteroceptors 287-288 motor unit 282-284,288 muscle contractions and 264 neurons 280-282,288 proprioceptors 285-287,289 receptors and reflexes 284-285

net force 57, 66-67, 106 neurons 281-282,288 neutralizer muscles 263-264 newton meters 131 newtons 50 Newton, Sir Isaac 44 Newton's laws of motion

action-reaction 109-110 angular momentum 180-187 overview 44-46 projectile motion 98-100, 102-105 static equilibrium and 67

Nike Sport Research Laboratory 12 Nordic ski racing 8,10-11 normal contact force 53-54

o Q'Brien, Parry 122 otoliths 286

P pacinian corpuscles 287, 289 pain receptors 287-288 pascals 215, 349 patellofemoral pain 362 pectineus muscle 22 pectoralis major muscle 22, 24 pelvis 19-21 pennate fibers 261,266-270,276 performance

biomechanics and 6-11, 298-300 center of gravity and 145-147 evaluation of 304-305 observation of 300-304

perimysium 257, 259 peripheral nervous system 280-281 phalanges 18-20 physiologic loading zone 351-352 pitching 306-310 pivot joints 245-246 planes, anatomical 25-29 plantar flexion 30-31,35,361-362 plastic behavior 228-229

INDEX

Poisson's ratio 226-227 pole vaulting 10-11,139-140,144,175-177 position 24,78-81,158-161,167 posterior, definition of 24 potential energy 117-119, 149-152 power 123-125,271-274,276-277 pressure 193-194,206,294,349,359-360 prestretch 274 principal axes 174-175 projectile motion 96-98,100-102,207-208 pronation 33-35,361-362 proprioceptors 284-287 proximal, definition of 24 proximal radioulnar joint 19-20 pubic symphysis 245-246 Pythagorean theorem 62, 64

Q Q angle 365-366 quadriceps femoris 263 qualitative anatomical analysis

football punt 331-335 javelin throwing 338-345 overview 325-329, 342 sprint running 334-339 vertical jump 330-331

quantum mechanics 41

R radial deviation 30, 32, 35 radians 160, 162 radioulnar joint 19-20,34 radius 18,20-21,165 radius of gyration 174,186

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range of motion 249-250,252,329,334-335,337-339,342 reaction forces 68-71,98, 103-104, 109-110,359-361 rearfoot motion 361 . reciprocal inhibition 286 rectilinear translation 76 rectus abdominis muscle 22, 24 rectus femoris muscle 22, 24 reference frames 78-80 reflexes 284-289 relativistic mechanics 40-41 remodeling 352-353 resultant displacement 81, 83-85 resultant force 57-62 ribs 19-21 right-hand thumb rule 160 righting reflex 287, 289 rigid-body mechanics 40-41,46 rotary (angular) inertia 172-178,186 running

anatomical analysis 334-338 angular momentum 180 average speed 86-89 biomechanical analysis 316-321 body mass 364-365 effect of road slope 357 foot structure and 365 knees and 365-366 loading patterns 358-362 overuse injuries 358-367

-running (continued)

position-time graph 361 Q angle 365-366 shoes 12,56,358-359,361,364-365 speed and injury 362-363 surfaces 363-364

Ryan, Nolan 90

S saddle joints 246 sagittal (anteroposterior) axis 26-27,30-33,35 sarcolemma 257, 259 sarcomeres 257-258,265,268-269,272-273,276 sartorius muscle 22, 24 scapula 18, 21 segments ofthe body 18-19 self-experiments

acceleration 100,103 angular motion 162,165,173,181,187 bending loads 221 buoyant force 193 center of gravity 141-142,145 deformation 233 elastic behavior 228 energy 117-119 friction 53-56 impulse and momentum 106-108 joint motion 251 lift force 203 linear motion 77-78 linear strain 225 moment of inertia 174 muscle contraction force 265-267,272,274 net force 104 projectile motion 97,102 reaction force 98-99,104,110 speed, velocity, and acceleration 89, 91-92 stress 215,218 stretch reflex 285 torque 129-130,132,135,137-138 work 114

semimembranosus muscle 23-24 semitendinosus muscle 23-24 sensory neurons 281 sesamoid bones 242 shear strain 226 shear stress 217-220,224,235,350 shock absorbance 122 shoes 12,56,358-359,361,364-365 shotput 106-107,121-122 shoulder

abduction 27-28 in javelin throwing 338,341,343 joint movement 30-34,246,330-331 overview 19-20 in sprint running 337, 339

sine function 65-66 skating 10-11,67-68,182 skeletal system 239-252. See also bonesi joints skiing 8,10-11,56-57 skull 19-20,246 soleus muscle 23-24

INDEX

somatic nervous system 281 space travel 352 specific gravity 194-195 speed 85:90,164 spin, ball 205-206 spinning actions 185 sport biomechanics. See biomechanical analysisi

biomechanics sprinting 175-176,316-321,334-339. See also running stability 147-154,151-153,248-252 stabilizer muscles 263 . stances 148-149,152-154 static equilibrium 67-72,136-140 static friction 53-56 statics 41 Steindler, Arthur 13 stiffness 234-235 stimulus duration 274-275,284 strain 118-119,225-227,235 streamlined shapes 200-202,204 strength 229-231,235-236,249-250 strength-training 134-136 stress 214-224

compression 217 continuum 351 definition of 214-215,235,349 in feet of runners 358-359 injury and 348-354 relaxation of 232-234 shear 217-220,224,235,350 stress-strain relationship 227-230,232,234-235 tension 215-216,220,230,235 tissue response to 350-353 WiUiams's model of 352-353

stretching exercises 234-235 stretch reflex 285-286,289 superficial, definition of 24 superior, definition of 24 supination 33-35,361-362 surface area 54-55,196 surface drag 198-199, 202 surface texture 200 swimming 7,195,203 swinging 71 synergy 264 synovial joints 245-251 Systeme-Internationale d'Unites (SI units) 42-43,46

T tangent function 65 tangential acceleration 166, 169 tarsals 19-20 technique improvement 6-8, 12,295-306. See also

performance tendon reflex 286 tendons 231,233-235,249,257-259 tennis 310-316 tensile forces 51,266-274,350 tensile strength 249-250 tensile stress 215-216,220,230,235 tension 215-216,223 thigh 18-19

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thorax 18-19 throwing sports 106-108,121-122,306-310 tibia 19-21 tibialis anterior muscle 22, 24 tightrope walking 186 time 42-43,326 tonic neck reflex 287-289 torque

angular momentum 183-188 examples of 131-133 force and 136 muscular 132-134,186,262-263,276 net 137-140 overview of 128-131,153

torsion load 223-224 toughness 229, 235 training 323-345. See also qualitative anatomical

analysis cross-training 364 improvement of 9-11 physical 325 technical 324-325

training effect 352-353 trajectories 96-98,100-102,207-208 transverse axis 26-27,30,34-35 trapezius muscle 23-24 triceps brachii muscle 19,23 trigonometry 64-67,84-85,369-378 trunk 31-34,340-341,344 turbulent flow 199-200,202 Type ITA muscle fibers (FOG) 275 Type IIB muscle fibers (FG) 275 Type I muscle fibers (SO) 275

U ulna 18,20-21 ulnar deviation 30,32,35 ultimate strength 229,235-236 uniaxialloads 219,235 uniaxial tension 224 units 42-43,46 upward rotation 33,35

V vastus intermedius muscle 24 vastus lateralis muscle 22, 24

INDEX

vastus medialis muscle 22, 24 vectors

acceleration 91-93 addition of 57-64 angular velocity 57-64, 163 components 96-98 definition of 50 displacement and 81,83-85 torque 131,139-140 velocity 88-89

velocity angular 163-166,181-182,187 average 88-89 of fastball pitch 307 injury and 362 instantaneous 89,318 linear 163-166 moment of inertia and 177-178 muscle contraction and 271-274 overview 85, 88-90 during performance 303 relative 196-197,202,208

vertebral column 19-21,227 vertical (longitudinal) axis 26-27,29,33,35 vertical motion 100-102 vestibular system 286-287,289 viscosity 198-199,202

W water pressure 193-194 watts 123-124 weight 43,59,69-70,364-365 weight-lifting 69-70,98-99,135-136,273-274. See also

arm curls; bench presses withdrawal reflex 288 Wolff'slaw 350-352,365 women, center of gravity 143 work 113-117,119-125 wrestling 132,134,154 wrist 19-23,31-32 Y yield strength 229, 235 Young's modulus 228,233 Z zero net force 98-100