Elementary Mechanics and Thermodynamics - J. Norbury

Elementary Mechanics and Thermodynamics - J. Norbury -...

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ELEMENTARY MECHANICS & THERMODYNAMICS Professor John W. Norbury Physics Department University of Wisconsin-Milwaukee P.O. Box 413 Milwaukee, WI 53201 November 20, 2000
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Contents 1 MOTION ALONG A STRAIGHT LINE 11 1.1 Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Position and Displacement . . . . . . . . . . . . . . . . . . . . 12 1.3 Average Velocity and Average Speed . . . . . . . . . . . . . . 14 1.4 Instantaneous Velocity and Speed . . . . . . . . . . . . . . . . 17 1.5 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Constant Acceleration: A Special Case . . . . . . . . . . . . . 20 1.7 Another Look at Constant Acceleration . . . . . . . . . . . . 23 1.8 Free-Fall Acceleration . . . . . . . . . . . . . . . . . . . . . . 24 1.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2 VECTORS 31 2.1 Vectors and Scalars . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Adding Vectors: Graphical Method . . . . . . . . . . . . . . . 33 2.3 Vectors and Their Components . . . . . . . . . . . . . . . . . 34 2.3.1 Review of Trigonometry . . . . . . . . . . . . . . . . . 34 2.3.2 Components of Vectors . . . . . . . . . . . . . . . . . 37 2.4 Unit Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5 Adding Vectors by Components . . . . . . . . . . . . . . . . . 41 2.6 Vectors and the Laws of Physics . . . . . . . . . . . . . . . . 43 2.7 Multiplying Vectors . . . . . . . . . . . . . . . . . . . . . . . 43 2.7.1 The Scalar Product (often called dot product) . . . . . 43 2.7.2 The Vector Product . . . . . . . . . . . . . . . . . . . 45 2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 MOTION IN 2 & 3 DIMENSIONS 47 3.1 Moving in Two or Three Dimensions . . . . . . . . . . . . . . 48 3.2 Position and Displacement . . . . . . . . . . . . . . . . . . . . 48 3.3 Velocity and Average Velocity . . . . . . . . . . . . . . . . . . 48 3
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4 CONTENTS 3.4 Acceleration and Average Acceleration . . . . . . . . . . . . . 49 3.5 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6 Projectile Motion Analyzed . . . . . . . . . . . . . . . . . . . 52 3.7 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . 58 3.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4 FORCE & MOTION - I 65 4.1 What Causes an Acceleration? . . . . . . . . . . . . . . . . . 66 4.2 Newton’s First Law . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.5 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . 66 4.6 Some Particular Forces . . . . . . . . . . . . . . . . . . . . . . 67 4.7 Newton’s Third Law . . . . . . . . . . . . . . . . . . . . . . . 68 4.8 Applying Newton’s Laws . . . . . . . . . . . . . . . . . . . . . 69 4.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 FORCE & MOTION - II 79 5.1 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2 Properties of Friction . . . . . . . . . . . . . . . . . . . . . . . 80 5.3 Drag Force and Terminal Speed . . . . . . . . . . . . . . . . . 82 5.4 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . 82 5.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6 POTENTIAL ENERGY & CONSERVATION OF ENERGY 89 6.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.3 Work-Energy Theorem . . . . . . . . . . . . . . . . . . . . . . 96 6.4 Gravitational Potential Energy . . . . . . . . . . . . . . . . . 98 6.5 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . 98 6.6 Spring Potential Energy . . . . . . . . . . . . . . . . . . . . . 101 6.7 Appendix: alternative method to obtain potential energy . . 103 6.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7 SYSTEMS OF PARTICLES 107 7.1 A Special Point . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.2 The Center of Mass . . . . . . . . . . . . . . . . . . . . . . . 108 7.3 Newton’s Second Law for a System of Particles . . . . . . . . 114 7.4 Linear Momentum of a Point Particle . . . . . . . . . . . . . 115 7.5 Linear Momentum of a System of Particles . . . . . . . . . . 115
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CONTENTS 5 7.6 Conservation of Linear Momentum . . . . . . . . . . . . . . . 116 7.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 8 COLLISIONS 119 8.1 What is a Collision? . . . . . . . . . . . . . . . . . . . . . . . 120 8.2 Impulse and Linear Momentum . . . . . . . . . . . . . . . . . 120 8.3 Elastic Collisions in 1-dimension . . . . . . . . . . . . . . . . 120 8.4 Inelastic Collisions in 1-dimension . . . . . . . . . . . . . . . 123 8.5 Collisions in 2-dimensions . . . . . . . . . . . . . . . . . . . . 124 8.6 Reactions and Decay Processes . . . . . . . . . . . . . . . . . 126 8.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9 ROTATION 131 9.1 Translation and Rotation . . . . . . . . . . . . . . . . . . . . 132 9.2 The Rotational Variables . . . . . . . . . . . . . . . . . . . . 132 9.3 Are Angular Quantities Vectors? . . . . . . . . . . . . . . . . 134 9.4 Rotation with Constant Angular Acceleration . . . . . . . . . 134 9.5 Relating the Linear and Angular Variables . . . . . . . . . . . 134 9.6 Kinetic Energy of Rotation . . . . . . . . . . . . . . . . . . . 135 9.7 Calculating the Rotational Inertia . . . . . . . . . . . . . . . 136 9.8 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 9.9 Newton’s Second Law for Rotation . . . . . . . . . . . . . . . 140 9.10 Work and Rotational Kinetic Energy . . . . . . . . . . . . . 140 9.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 10 ROLLING, TORQUE & ANGULAR MOMENTUM 145 10.1 Rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 10.2 Yo-Yo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 10.3 Torque Revisited . . . . . . . . . . . . . . . . . . . . . . . . . 148 10.4 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . 148 10.5 Newton’s Second Law in Angular Form . . . . . . . . . . . . 148 10.6 Angular Momentum of a System of Particles . . . . . . . . . 149 10.7 Angular Momentum of a Rigid Body Rotating About a Fixed Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 10.8 Conservation of Angular Momentum . . . . . . . . . . . . . . 149 10.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 11 GRAVITATION 153 11.1 The World and the Gravitational Force . . . . . . . . . . . . 158 11.2 Newton’s Law of Gravitation . . . . . . . . . . . . . . . . . . 158
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6 CONTENTS 11.3 Gravitation and Principle of Superposition
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