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Biomechanics of Sport and Exercise, 3E

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Biomechanics of Sport and Exercise, 3E Contents Copyright page Preface Acknowledgments Student and Instructor Resources How to Use MaxTRAQ Inside front cover and end sheet Chapter Introduction: Why Study Biomechanics? What Is Biomechanics? What Are the Goals of Sport and Exercise Biomechanics? The History of Sport Biomechanics The Organization of Mechanics Basic Dimensions and Units of Measurement Used in Mechanics Summary Part I: External Biomechanics Chapter 1: Forces: Maintaining Equilibrium or Changing Motion What Are Forces? Classifying Forces Friction Addition of Forces: Force Composition Resolution of Forces Static Equilibrium Summary Chapter 2: Linear Kinematics: Describing Objects in Linear Motion Motion Linear Kinematics Uniform Acceleration and Projectile Motion Summary Chapter 3: Linear Kinetics: Explaining the Causes of Linear Motion Newton’s First Law of Motion: Law of Inertia Conservation of Momentum Newton’s Second Law of Motion: Law of Acceleration Impulse and Momentum Newton’s Third Law of Motion: Law of Action-Reaction Newton’s Law of Universal Gravitation Summary Chapter 4: Work, Power, and Energy Work Energy The Work–Energy Relationship Power Summary Chapter 5: Torques and Moments of Force What Are Torques? Forces and Torques in Equilibrium What Is Center of Gravity? Summary Chapter 6: Angular Kinematics Angular Position and Displacement Angular and Linear Displacement Angular Velocity Angular and Linear Velocity Angular Acceleration Angular and Linear Acceleration Anatomical System for Describing Limb Movements Summary Chapter 7: Angular Kinetics Angular Inertia Angular Momentum Angular Interpretation of Newton’s First Law of Motion Angular Interpretation of Newton’s Second Law of Motion Angular Impulse and Angular Momentum Angular Interpretation of Newton’s Third Law of Motion Summary Chapter 8: Fluid Mechanics Buoyant Force: Force Due to Immersion Dynamic Fluid Force: Force Due to Relative Motion Summary Part II: Internal Biomechanics Chapter 9: Mechanics of Biological Materials Stress Strain Mechanical Properties of Materials: The Stress–Strain Relationship Mechanical Properties of the Musculoskeletal System Summary Chapter 10: The Skeletal System Bones Joints Summary Chapter 11: The Muscular System The Structure of Skeletal Muscle Muscle Action Muscle Contraction Force Summary Chapter 12: The Nervous System The Nervous System and the Neuron The Motor Unit Receptors and Reflexes Summary Part III: Applying Biomechanical Principles Chapter 13: Qualitative Biomechanical Analysis to Improve Technique Types of Biomechanical Analysis Steps of a Qualitative Biomechanical Analysis Sample Analyses Summary Chapter 14: Qualitative Biomechanical Analysis to Improve Training Biomechanics and Training Qualitative Anatomical Analysis Method Sample Analyses Summary Chapter 15: Qualitative Biomechanical Analysis to Understand Injury Development Mechanical Stress and Injury Tissue Response to Stress Mechanism of Overuse Injury Individual Differences in Tissue Threshold Intrinsic and Extrinsic Factors Affecting Injury Sample Analysis: Overuse Injuries in Running Summary Chapter 16: Technology in Biomechanics Quantitative Biomechanical Analysis Measurement Issues Tools for Measuring Biomechanical Variables Summary Appendix A Appendix B Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Glossary References and Suggested Readings Web Resources About the Author Quick Reference Equations Mathematical Formulas Pythagorean theorem A 2 + B 2 = C 2 (1.5) Trigonometric functions (1.6) (1.7) (1.8) (1.9) (1.10) (1.11) Linear Kinematics Average speed (2.5) Average velocity (2.6) Average acceleration (2.9) Projectile Equations Vertical motion (y) Vertical position: (2.14) if y i = 0 and v i = 0 (2.16) Vertical velocity: v f = v i + gΔt (2.11) v 2 = v 2 + 2gΔy (2.15) v peak = 0 (2.19) v f = gΔt if y i = 0 and v i = 0 (2.17) 2 v = 2gΔy if v i = 0 (2.18) Vertical acceleration: a = g = −9.81 m/s2 (2.10) Horizontal motion (x) Horizontal position: x = vΔt (2.26) Horizontal velocity: v = v f = v i = constant (2.22) Horizontal acceleration: a = 0 (2.23) Other equations governing projectile motion Time of flight: Δt up = Δt down if y f = y i (2.20) Δt flight = 2Δt up if y f = y i (2.21) Parabolic equation: (2.27) Linear Kinetics Weight W = mg (1.2) Static and dynamic friction F s = μs R (1.3) F d = μd R (1.4) Static equilibrium ΣF = 0 (1.12) ΣF x = 0 (1.13) ΣF y = 0 (1.14) Newton’s 1st law: law of inertia v = constant if ΣF = 0 (3.1a) or ΣF = 0 if v = constant (3.1b) Linear momentum L = mv (3.6) Conservation of momentum L = constant if ΣF = 0 (3.7) L x = constant if ΣF x = 0 (3.8) L y = constant if ΣF y = 0 (3.9) L i = Σ(mu) = m 1 u 1 + m 2 u 2 + m 3 u 3 + . = m 1 v 1 + m 2 v 2 + m 3 v 3 + . = Σ(mv) = L f = constant if Σ F = 0 (3.11) Perfectly elastic collision of two objects (3.17) Perfectly inelastic collision of two objects m 1 u 1 + m 2 u 2 = (m 1 + m 2)v (3.19) Coefficient of restitution (3.20) Newton’s 2nd law: law of acceleration ΣF = ma (3.22) ΣF x = ma x (3.23) ΣF y = ma y (3.24) Impulse–momentum equation Σ Δt = m(v f − v i) (3.29) Universal law of gravitation: gravitational force (3.30) Work, Power, and Energy Work U = (d) (4.2) Kinetic energy (4.4) Gravitational potential energy PE = Wh (4.5) Strain energy (4.7) Work–energy principle U = ΔE (4.8) Power (4.12) P = (4.13) Angular Kinematics Angular position measured in radians (6.1) Angular displacement and arc length ℓ = Δθr (6.4) Average angular velocity (6.6) Angular velocity and linear velocity v T = ωr (6.8) Average angular acceleration (6.9) Tangential acceleration a T = αr (6.10) Centripetal acceleration (6.11) 2 a r = ω r (6.12) Angular Kinetics Torque T = F × r (5.1) Static equilibrium ΣT = 0 (5.2) Center of gravity Σ(W × r) = (ΣW) × r cg (5.3) Moment of inertia 2 I a = Σm i r i (7.1) 2 I a = mk a (7.2) Moment of inertia: parallel axis theorem 2 I b = I cg + mr (7.3) Angular momentum H a = I a ω a (7.4) Angular momentum of the human body 2 H a = Σ(I i ω i + m i r i/cg ω i/cg) (7.5) Conservation of angular momentum H i = I i ω i = I f ω f = H f = constant if ΣT = 0 (7.7) Angular version of Newton’s 2nd law ΣT a = I a α a (7.9) (7.10) Angular impulse-momentum Σ aΔt = (H f – H i)a (7.11) Fluid Mechanics Pressure P = F/A Density (8.3) Drag force (8.5) Lift force (8.6) Mechanics of Materials Stress (9.1) Shear stress (9.2) Strain (9.4) Elastic modulus (9.5) Abbreviations for Variables and Subscripts Used in Equations Variables a = instantaneous linear acceleration = average linear acceleration A = area C D = coefficient of drag C L = coefficient of lift d = displacement e = coefficient of restitution E = energy E = elastic modulus or Young’s modulus F = force = average force F d = dynamic friction force F s = static friction force ΣF = net force = sum of forces g = acceleration due to gravity G = gravitational constant h = height H = angular momentum I = moment of inertia k = radius of gyration k = stiffness or spring constant KE = kinetic energy ℓ = distance traveled or length L = linear momentum m = mass P = power P = pressure P = force PE = gravitational potential energy r = radius r = moment arm R = normal contact force s = instantaneous linear speed = average linear speed t = time T = torque u = pre-impact velocity U = work done v = instantaneous linear velocity v = post-impact velocity = average linear velocity V = volume W = weight x = horizontal position y = vertical position α = instantaneous angular acceleration = average angular acceleration Δ = change in . = final – initial ε = strain μ = coefficient of friction ρ = density σ = stress Σ = sum of … τ = shear stress θ = angular position ω = instantaneous angular velocity = average angular velocity Subscripts a = axis b = axis d = dynamic cg = center of gravity D = drag f = final or ending i = initial or starting i = one of a number of parts L = lift o = original or undeformed r = radial s = static T = tangential x = horizontal y = vertical Introduction Why Study Biomechanics? © Lukas Blazek | Dreamstime.com Objectives When you finish reading this introduction, you should be able to do the following: Define biomechanics Define sport and exercise biomechanics Identify the goals of sport and exercise biomechanics Describe the methods used to achieve the goals of sport and exercise biomechanics Be somewhat familiar with the history and development of sport and exercise biomechanics Define mechanics Outline the organization of mechanics Define length and the units of measurement for length Define time and the units of measurement for time Define mass and the units of measurement for mass You are watching the Olympic Games on television when you see a high jumper successfully jump over a crossbar set more than a foot above his head. The technique he uses looks very awkward. He approaches the bar from the side, and when he jumps off the ground he turns his back toward the bar. His head and arms clear the bar first; he then arches his back and finally kicks his legs out and up to get them over the bar. He lands in the pit in an ungainly position: on his shoulders and back with his legs extended in the air above him. You think to yourself, How can he jump so high using such an odd-looking technique? Certainly, there must be another technique that is both more effective and more graceful looking.
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