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Elementary Mechanics and Thermodynamics

Oct 14, 2014

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ELEMENTARYMECHANICS & THERMODYNAMICSProfessor John W. NorburyPhysics DepartmentUniversity of Wisconsin-MilwaukeeP.O. Box 413Milwaukee, WI 53201November 20, 20002Contents1 MOTION ALONG A STRAIGHT LINE 111.1 Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2 Position and Displacement . . . . . . . . . . . . . . . . . . . . 121.3 Average Velocity and Average Speed . . . . . . . . . . . . . . 141.4 Instantaneous Velocity and Speed . . . . . . . . . . . . . . . . 171.5 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.6 Constant Acceleration: A Special Case . . . . . . . . . . . . . 201.7 Another Look at Constant Acceleration . . . . . . . . . . . . 231.8 Free-Fall Acceleration . . . . . . . . . . . . . . . . . . . . . . 241.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 VECTORS 312.1 Vectors and Scalars . . . . . . . . . . . . . . . . . . . . . . . . 322.2 Adding Vectors: Graphical Method . . . . . . . . . . . . . . . 332.3 Vectors and Their Components . . . . . . . . . . . . . . . . . 342.3.1 Review of Trigonometry . . . . . . . . . . . . . . . . . 342.3.2 Components of Vectors . . . . . . . . . . . . . . . . . 372.4 Unit Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.5 Adding Vectors by Components . . . . . . . . . . . . . . . . . 412.6 Vectors and the Laws of Physics . . . . . . . . . . . . . . . . 432.7 Multiplying Vectors . . . . . . . . . . . . . . . . . . . . . . . 432.7.1 The Scalar Product (often called dot product) . . . . . 432.7.2 The Vector Product . . . . . . . . . . . . . . . . . . . 452.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 MOTION IN 2 & 3 DIMENSIONS 473.1 Moving in Two or Three Dimensions . . . . . . . . . . . . . . 483.2 Position and Displacement . . . . . . . . . . . . . . . . . . . . 483.3 Velocity and Average Velocity . . . . . . . . . . . . . . . . . . 4834 CONTENTS3.4 Acceleration and Average Acceleration . . . . . . . . . . . . . 493.5 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . 513.6 Projectile Motion Analyzed . . . . . . . . . . . . . . . . . . . 523.7 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . 583.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 FORCE & MOTION - I 654.1 What Causes an Acceleration? . . . . . . . . . . . . . . . . . 664.2 Newtons First Law . . . . . . . . . . . . . . . . . . . . . . . . 664.3 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.5 Newtons Second Law . . . . . . . . . . . . . . . . . . . . . . 664.6 Some Particular Forces . . . . . . . . . . . . . . . . . . . . . . 674.7 Newtons Third Law . . . . . . . . . . . . . . . . . . . . . . . 684.8 Applying Newtons Laws . . . . . . . . . . . . . . . . . . . . . 694.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 FORCE & MOTION - II 795.1 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.2 Properties of Friction . . . . . . . . . . . . . . . . . . . . . . . 805.3 Drag Force and Terminal Speed . . . . . . . . . . . . . . . . . 825.4 Uniform Circular Motion . . . . . . . . . . . . . . . . . . . . 825.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856 POTENTIAL ENERGY & CONSERVATION OF ENERGY 896.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.2 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 926.3 Work-Energy Theorem . . . . . . . . . . . . . . . . . . . . . . 966.4 Gravitational Potential Energy . . . . . . . . . . . . . . . . . 986.5 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . 986.6 Spring Potential Energy . . . . . . . . . . . . . . . . . . . . . 1016.7 Appendix: alternative method to obtain potential energy . . 1036.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057 SYSTEMS OF PARTICLES 1077.1 A Special Point . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.2 The Center of Mass . . . . . . . . . . . . . . . . . . . . . . . 1087.3 Newtons Second Law for a System of Particles . . . . . . . . 1147.4 Linear Momentum of a Point Particle . . . . . . . . . . . . . 1157.5 Linear Momentum of a System of Particles . . . . . . . . . . 115CONTENTS 57.6 Conservation of Linear Momentum . . . . . . . . . . . . . . . 1167.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1188 COLLISIONS 1198.1 What is a Collision? . . . . . . . . . . . . . . . . . . . . . . . 1208.2 Impulse and Linear Momentum . . . . . . . . . . . . . . . . . 1208.3 Elastic Collisions in 1-dimension . . . . . . . . . . . . . . . . 1208.4 Inelastic Collisions in 1-dimension . . . . . . . . . . . . . . . 1238.5 Collisions in 2-dimensions . . . . . . . . . . . . . . . . . . . . 1248.6 Reactions and Decay Processes . . . . . . . . . . . . . . . . . 1268.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1299 ROTATION 1319.1 Translation and Rotation . . . . . . . . . . . . . . . . . . . . 1329.2 The Rotational Variables . . . . . . . . . . . . . . . . . . . . 1329.3 Are Angular Quantities Vectors? . . . . . . . . . . . . . . . . 1349.4 Rotation with Constant Angular Acceleration . . . . . . . . . 1349.5 Relating the Linear and Angular Variables . . . . . . . . . . . 1349.6 Kinetic Energy of Rotation . . . . . . . . . . . . . . . . . . . 1359.7 Calculating the Rotational Inertia . . . . . . . . . . . . . . . 1369.8 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1409.9 Newtons Second Law for Rotation . . . . . . . . . . . . . . . 1409.10 Work and Rotational Kinetic Energy . . . . . . . . . . . . . 1409.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14210 ROLLING, TORQUE & ANGULAR MOMENTUM 14510.1 Rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14610.2 Yo-Yo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14710.3 Torque Revisited . . . . . . . . . . . . . . . . . . . . . . . . . 14810.4 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . 14810.5 Newtons Second Law in Angular Form . . . . . . . . . . . . 14810.6 Angular Momentum of a System of Particles . .