**Introduction 1**

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 3

Beyond the Book 3

Where to Go from Here 4

**Part I: Getting Started with Biomechanics 5**

**Chapter 1: Jumping Into Biomechanics 7**

Analyzing Movement with Biomechanics 7

Mechanics 8

Bio 9

Expanding on Mechanics 10

Describing motion with kinematics 11

Causing motion with kinetics 13

Putting Biomechanics to Work 14

**Chapter 2: Reviewing the Math You Need for Biomechanics 15**

Getting Orientated 16

Brushing Up on Algebra 17

Following the order of operations 17

Defining some math operations 19

Isolating a variable 20

Interpreting proportionality 22

Looking for the Hypotenuse 23

Using the Pythagorean theorem 24

De-tricking trigonometric functions: SOH CAH TOA 26

Unvexing Vector Quantities 31

Resolving a vector into components 33

Composing a vector from components 35

**Chapter 3: Speaking the Language of Biomechanics 37**

Measuring Scalars and Vectors 38

Standardizing a Reference Frame 39

Directing your attention to locations of the body 40

Referencing planes and axes 40

Describing Movement: Kinematics 42

Typecasting motion: Linear, angular, and general 42

Describing how far: Distance and displacement 43

Describing how fast: Speed and velocity 44

Changing velocity: Acceleration 45

Pushing and Pulling into Kinetics 45

Forcing yourself to understand Newton's laws of motion 47

Using the impulse-momentum relationship 49

Working with Energy and Power 49

Mechanical work 49

Mechanical energy 50

Mechanical power 51

Turning Force into Torque 51

Dealing with Measurement Units 51

Using the Neuromusculoskeletal System to Move 52

The skeletal system 53

The muscular system 53

The nervous system 55

**Part II: Looking At Linear Mechanics 57**

**Chapter 4: Making Motion Change: Force 59**

Pushing and Pulling: What Is Force? 59

Working with Force Vectors 65

Using the force components to find the resultant 66

Resolving a force into components 68

Classifying Forces 69

Contact and noncontact forces 69

Internal and external forces 70

Feeling the Pull of Gravity 74

Slipping, Sliding, and Staying Put: Friction Is F N 76

Materials do matter: The coefficient of friction ( ) 80

Squeezing to stick: Normal reaction force (N) 81

**Chapter 5: Describing Linear Motion: Linear Kinematics 83**

Identifying Position 84

Describing How Far a Body Travels 85

Distance.85

Displacement 86

Describing How Fast a Body Travels 88

Speed 89

Velocity 90

Momentum 92

Speeding Up or Slowing Down: Acceleration 92

Constant acceleration 95

Projectile motion 95

**Chapter 6: Causing Linear Motion: Linear Kinetics 103**

Clarifying Net Force and Unbalanced Force 103

Newton's First Law: The Law of Inertia 106

Newton's Third Law: The Law of Equal and Opposite Action-Reaction 107

Newton's Second Law: The Law of Acceleration 109

Deriving the impulse-momentum relationship from the law of acceleration 112

Applying the impulse-momentum relationship for movement analysis 114

**Chapter 7: Looking At Force and Motion Another Way: Work, Energy, and Power 119**

Working with Force 120

Energizing Movement 122

Kinetic energy 123

Potential energy 124

Conserving Mechanical Energy 128

Powering Better Performance 130

The Work-Energy Relationship 131

**Part III: Investigating Angular Mechanics 137**

**Chapter 8: Twisting and Turning: Torques and Moments of Force 139**

Defining Torque 140

Lining up for rotation: The moment arm of a force 141

Calculating the turning effect of a force 142

Measuring Torque 144

Muscling into torque: How muscles serve as torque generators 145

Resisting torque: External torques on the body 148

Expanding on Equilibrium: Balanced Forces and Torques 149

Locating the Center of Gravity of a Body 152

**Chapter 9: Angling into Rotation: Angular Kinematics 157**

Measuring Angular Position 157

Describing How Far a Body Rotates 160

Angular distance 161

Angular displacement 162

Describing How Fast a Body Rotates 163

Angular speed.163

Angular velocity 164

Speeding Up or Slowing Down: Angular Acceleration 165

Relating Angular Motion to Linear Motion 167

Angular displacement and linear displacement 168

Angular velocity and linear velocity 169

Angular acceleration and linear acceleration 171

**Chapter 10: Causing Angular Motion: Angular Kinetics 173**

Resisting Angular Motion: The Moment of Inertia 174

The moment of inertia of a segment174

The moment of inertia of the whole body 178

Considering Angular Momentum 180

Angular momentum of a rigid body 180

Angular momentum of the human body when individual segments rotate 181

A New Angle on Newton: Angular Versions of Newton's Laws 181

Maintaining angular momentum: Newton's first law.182

Changing angular momentum: Newton's second law 186

Equal but opposite: Newton's third law189

Changing Angular Momentum with Angular Impulse 191

**Chapter 11: Fluid Mechanics 193**

Buoyancy: Floating Along 193

Considering Force Due to Motion in Fluid 197

Causing drag in a fluid 198

Causing lift in a fluid 201

**Part IV: Analyzing the Bio of Biomechanics 205**

**Chapter 12: Stressing and Straining: The Mechanics of Materials 207**

Visualizing Internal Loading of a Body 208

Applying Internal Force: Stress 210

Normal stress 212

Shear stress 217

Responding to Internal Force: Strain 219

Determining tensile strain 221

Determining compressive strain 221

Determining shear strain 222

Straining from Stress: The Stress-Strain Relationship 223

Give and go: Behaving elastically 224

Give and stay: Behaving plastically 224

**Chapter 13: Boning Up on Skeletal Biomechanics 227**

What the Skeletal System Does 228

How Bones Are Classified 228

The Materials and Structure of Bones 230

Materials: What bones are made of 231

Structure: How bones are organized 232

Connecting Bones: Joints 234

Immovable joints 234

Slightly movable joints 234

Freely movable joints 235

Growing and Changing Bone 237

Changing bone dimensions 238

Stressing bone: The effects of physical activity and inactivity 239

**Chapter 14: Touching a Nerve: Neural Considerations in Biomechanics 247**

Monitoring and Controlling the Body: The Roles of the Nervous System 248

Outlining the Nervous System 248

The central nervous system 250

The peripheral nervous system 250

Zeroing In on Neurons 251

Parts of neurons 251

Types of neurons 251

Controlling Motor Units 259

Motor unit recruitment 261

Rate coding 261

**Chapter 15: Muscling Segments Around: Muscle Biomechanics 263**

Characterizing Muscle 263

Seeing How Skeletal Muscles Are Structured 265

The macrostructure of muscles 266

The microstructure of muscle fibers.268

Comparing Types of Muscle Activity 270

Isometric activity 271

Concentric activity 272

Eccentric activity 272

Producing Muscle Force 274

Relating muscle length and tension 274

Relating muscle velocity and tension277

Stretching before Shortening: The Key to Optimal Muscle Force 279

**Part V: Applying Biomechanics 283**

**Chapter 16: Eyeballing Performance: Qualitative Analysis 285**

Serving as a Movement Analyst 286

Evaluating the Performance 287

Identifying the goal of the movement 287

Specifying the mechanical objective 289

Determining whether the goal has been reached 290

Troubleshooting the Performance 293

Constraints on performance 293

Technique errors 294

Pitching by the phases 298

Intervening to Improve the Performance 302

Adapting the constraints on throwing performance 302

Refining technique 303

**Chapter 17: Putting a Number on Performance: Quantitative Analysis 305**

Converting Continuous Data to Numbers 305

Measuring Kinematics: Motion-Capture Systems 306

Collecting kinematic data 307

Processing kinematic data 308

Measuring Kinetics: Force Platform Systems 310

Collecting kinetic data 310

Processing kinetic data 312

Recording Muscle Activity: Electromyography 313

Collecting the electromyogram 314

Processing the electromyogram 315

**Chapter 18: Furthering Biomechanics: Research Applications 319**

Exercising in Space 319

Repairing the Anterior Cruciate Ligament 320

Running Like Our Ancestors 322

Protecting Our Beans: Helmet Design 324

Balancing on Two Legs: Harder Than You Think 326

**Chapter 19: Investigating Forensic Biomechanics: How Did It Happen? 329**

Collecting Information for a Forensic Biomechanics Analysis 330

Witness accounts 330

Police incident investigation reports 331

Medical records 331

Determining the Mechanism of Injury 332

Evaluating Different Scenarios 335

Ending up on the far side of the road 335

Landing in water with a broken jaw 336

**Part VI: The Parts of Tens 339**

**Chapter 20: Ten Online Resources for Biomechanics 341**

The Exploratorium 341

The Physics Classroom 341

Coaches Info 342

Textbook-Related Websites 343

Topend Sports 343

Dr. Mike Marshall's Pitching Coach Services 343

Waterloo's Dr. Spine, Stuart McGill 344

Skeletal Bio Lab 345

Biomch-L 345

American Society of Biomechanics 346

**Chapter 21: Ten Things You May Not Know about Biomechanics 347**

Looking at How Biomechanics Got Its Start 347

Adding Realism to Entertainment 348

Developing Safer Motor Vehicles 348

Improving the On-Shelf Quality of Fruits and Vegetables 349

Fitting Footwear to the Activity 350

Banning Biomechanically Improved Sport Techniques 351

Re-Creating Dinosaurs 352

Designing Universally and Ergonomically 352

Giving a Hand to Prosthetics Design 353

Losing Weight to Help Your Joints 354

**Chapter 22: Ten Ways to Succeed in Your Biomechanics Course 355**

Go to Class and Ask Questions 355

Read the Textbook 356

Do the Problems and Review Questions at the End of the Chapter 357

Create Flashcards 357

Go to Office Hours 358

Form a Study Group with Classmates 358

Accept and Apply Newton as the Foundation of Movement Analysis 359

Talk Fluent Biomechanics with Your Classmates 359

Volunteer for Research Projects 360

Attend a Biomechanics Conference 361

Index 363