WORKED EXAMPLES FROM INTRODUCTORY PHYSICS (ALGEBRA-BASED): BASIC MECHANICS

By ANDREW MOORE

CONTENTS MATHEMATICAL CONCEPTS THE IMPORTANT STU? MEASUREMENT AND UNITS IN PHYSICS THE METRIC SYSTEM; CONVERTING UNITS MATH: YOU HAD THIS IN HIGH SCHOOL OH, YES YOU DID MATH: TRIGONOMETRY VECTORS AND VECTOR ADDITION COMPONENTS OF VECTORS WORKED EXAMPLES MEASUREMENT AND UNITS TRIGONOMETRY MOTION IN ONE DIMENSION DISPLACEMENT SPEED AND VELOCITY MOTION WITH CONSTANT VELOCITY ACCELERATION MOTION WHERE THE ACCELERATION IS CONSTANT FREE-FALL MOTION IN TWO DIMENSIONS MOTION IN TWO DIMENSIONS, COORDINATES AND DISPLACEMENT VELOCITY AND ACCELERATION MOTION WHEN THE ACCELERATION IS CONSTANT FREE FALL; PROJECTILE PROBLEMS GROUND–TO–GROUND PROJECTILE: A LONG EXAMPLE MOTION FOR CONSTANT ACCELERATION FREE–FALL; PROJECTILE PROBLEMS FORCES I INTRODUCTION NEWTON’S 1ST LAW NEWTON’S 2ND LAW UNITS AND STU? NEWTON’S 3RD LAW THE FORCE OF GRAVITY OTHER FORCES WHICH APPEAR IN OUR PROBLEMS THE FREE–BODY DIAGRAM: DRAW THE DAMN PICTURE! SIMPLE EXAMPLE: WHAT DOES THE SCALE READ? 4 1 10 AN IMPORTANT EXAMPLE: MASS SLIDING ON A SMOOTH INCLINED PLANE 4 1 11 ANOTHER IMPORTANT EXAMPLE: THE ATTWOOD MACHINE NEWTON’S SECOND LAW APPLYING NEWTON’S LAWS OF MOTION FORCES II FRICTION FORCES AN IMPORTANT EXAMPLE: BLOCK SLIDING DOWN ROUGH INCLINED PLANE UNIFORM CIRCULAR MOTION CIRCULAR MOTION AND FORCE ORBITAL MOTION ENERGY KINETIC ENERGY WORK THE WORK–ENERGY THEOREM POTENTIAL ENERGY THE SPRING FORCE THE PRINCIPLE OF ENERGY CONSERVATION SOLVING PROBLEMS WITH ENERGY CONSERVATION POWER MOMENTUM MOMENTUM; SYSTEMS OF PARTICLES RELATION TO FORCE; IMPULSE THE PRINCIPLE OF MOMENTUM CONSERVATION COLLISIONS; PROBLEMS USING THE CONSERVATION OF MOMENTUM SYSTEMS OF PARTICLES; THE CENTER OF MASS FINDING THE CENTER OF MASS ROTATIONAL KINEMATICS RIGID BODIES; ROTATING OBJECTS ANGULAR DISPLACEMENT ANGULAR VELOCITY ANGULAR ACCELERATION THE CASE OF CONSTANT ANGULAR ACCELERATION RELATION BETWEEN ANGULAR AND LINEAR QUANTITIES ANGULAR VELOCITY AND ACCELERATION ROTATIONAL MOTION WITH CONSTANT ANGULAR ACCELERATION ROTATIONAL DYNAMICS ROTATIONAL KINETIC ENERGY MORE ON THE MOMENT OF INERTIA TORQUE ANOTHER WAY TO LOOK AT TORQUE NEWTON’S 2ND LAW FOR ROTATIONS SOLVING PROBLEMS WITH FORCES, TORQUES AND ROTATING OBJECTS AN EXAMPLE STATICS 9 1 10 ROLLING MOTION 9 1 11 EXAMPLE: ROUND OBJECT ROLLS DOWN SLOPE WITHOUT SLIPPING 9 1 12 ANGULAR MOMENTUM THE MOMENT OF INERTIA AND ROTATIONAL KINETIC ENERGY 10 OSCILLATORY MOTION 10 1 THE IMPORTANT STU? 10 1 1 INTRODUCTION 10 1 2 HARMONIC MOTION 10 1 3 DISPLACEMENT, VELOCITY AND ACCELERATION 10 1 4 THE REFERENCE CIRCLE 10 1 5 A REAL MASS/SPRING SYSTEM 10 1 6 ENERGY AND THE HARMONIC OSCILLATOR 10 1 7 SIMPLE PENDULUM 10 1 8 PHYSICAL PENDULUM 10 2 WORKED EXAMPLES 10 2 1 HARMONIC MOTION 10 2 2 MASS–SPRING SYSTEM 10 2 3 SIMPLE PENDULUM 11 WAVES I 11 1 THE IMPORTANT STU? 11 1 1 INTRODUCTION 11 1 2 PRINCIPLE OF SUPERPOSITION 11 1 3 HARMONIC WAVES 11 1 4 WAVES ON A STRING 11 1 5 SOUND WAVES 11 1 6 SOUND INTENSITY 11 1 7 THE DOPPLER E?ECT 11 2 WORKED EXAMPLES 11 2 1 HARMONIC WAVES 11 2 2 WAVES ON A STRING 11 2 3 SOUND WAVES