Guide to Classical Physics: Using Mathematica for Calculations and Visualizations

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
CHAPTER 1: Units
	1.1. LENGTH
	1.2. TIME
	1.3. MASS
	1.4. OTHER BASE UNITS
		1.4.1. Temperature
		1.4.2. Electric Current
		1.4.3. Quantity
		1.4.4. Luminous Intensity
	1.5. METRIC ABBREVIATIONS
	1.6. DERIVED UNITS
	1.7. NON-METRIC UNITS
	1.8. SIGNIFICANT FIGURES
	1.9. PHYSICAL CONSTANTS
CHAPTER 2: Functions
	2.1. TRIGONOMETRIC FUNCTIONS
	2.2. DEGREES TO RADIANS
	2.3. INVERSE TRIGONOMETRIC FUNCTIONS
	2.4. EXPONENTIAL FUNCTION
	2.5. USER-DEFINED FUNCTION
	2.6. DIFFERENTIATION
	2.7. INTEGRATION
		2.7.1. Indefinite Integrals
		2.7.2. Definite Integrals
CHAPTER 3: Vectors
	3.1. UNIT VECTORS
	3.2. SCALAR-PRODUCT
	3.3. SQUARE OF THE MAGNITUDE
	3.4. COSINE RULE FOR DOT PRODUCT
	3.5. ADDING AND SUBTRACTING VECTORS
	3.6. VECTOR PRODUCT
	3.7. SINE RULE FOR CROSS PRODUCT
	3.8. VECTOR EQUATIONS
	3.9. TRIPLE VECTOR PRODUCT
CHAPTER 4: Motion in One Dimension
	4.1. POSITION
		4.1.1. Role of Time
		4.1.2. Displacement
	4.2. VELOCITY
		4.2.1. Average Velocity
		4.2.2. Instantaneous Velocity
		4.2.3. Speed
	4.3. ACCELERATION
		4.3.1. Average Acceleration
		4.3.2. Instantaneous Acceleration
	4.4. ANOTHER EXAMPLE
	4.5. CONSTANT ACCELERATION
		4.5.1. Equation with No Time
		4.5.2. Average Velocity
		4.5.3. Free Fall
	4.6. COMPARING THE MOTION OF TWO OBJECTS
CHAPTER 5: Motion in Two and Three Dimensions
	5.1. THE VECTORS
	5.2. PROJECTILE MOTION
		5.2.1. Range
		5.2.2. The Monkey Problem
	5.3. CHARGED PARTICLE IN A MAGNETIC FIELD
CHAPTER 6: Newton’s Laws
	6.1. FORCES
	6.2. FIRST LAW
	6.3. SECOND LAW
	6.4. THIRD LAW
	6.5. FREE-BODY DIAGRAMS
		6.5.1. Free-Fall
		6.5.2. Tension
		6.5.3. Pulley
	6.6. FRICTION
		6.6.1. Pulley Problem
		6.6.2. Mass Pinned Against a Wall
	6.7. BLOCK ON INCLINED PLANE
		6.7.1. No Friction
		6.7.2. Static Friction
		6.7.3. Kinetic Friction
	6.8. UNIFORM CIRCULAR MOTION
		6.8.1. Object Connected to a String
		6.8.2. Car Rounding a Curve
	6.9. SIMPLE HARMONIC MOTION
CHAPTER 7: Energy
	7.1. WORK
	7.2. KINETIC ENERGY
	7.3. WORK-KINETIC ENERGY THEOREM
	7.4. POWER
	7.5. POTENTIAL ENERGY
	7.6. ENERGY CONSERVATION
CHAPTER 8: Momentum
	8.1. LINEAR MOMENTUM
	8.2. IMPULSE
	8.3. MOMENTUM CONSERVATION
		8.3.1. Block Sliding on a Wedge
	8.4. COLLISIONS
		8.4.1. Ballistic Pendulum
		8.4.2. Billiard Balls
CHAPTER 9: Rotational Motion
	9.1. ANGLE
	9.2. ANGULAR VELOCITY
	9.3. ANGULAR ACCELERATION
	9.4. CONSTANT ANGULAR ACCELERATION
	9.5. MOMENT OF INERTIA
		9.5.1. Stick
		9.5.2. Cylinder
		9.5.3. Disk
		9.5.4. Sphere
		9.5.5. Ball
	9.6. CONSERVATION OF ENERGY
	9.7. TORQUE
		9.7.1. Definition
		9.7.2. Newton’s Second Law
	9.8. ANGULAR MOMENTUM
	9.9. ROLLING WITHOUT SLIPPING
	9.10. CONSERVATION OF ANGULAR MOMENTUM
CHAPTER 10: Universal Gravitation
	10.1. UNIVERSAL FORCE LAW
	10.2. POTENTIAL ENERGY
	10.3. GRAVITATIONAL FORCE FROM A SPHERE
		10.3.1. Ring of Mass
		10.3.2. Sphere of Mass
		10.3.3. Oscillating Mass
	10.4. KEPLER’S LAWS
		10.4.1. Law of Orbits
		10.4.2. Law of Areas
		10.4.3. Law of Periods
CHAPTER 11: Fluids
	11.1. DENSITY AND PRESSURE
		11.1.1. Water
		11.1.2. Air
		11.1.3. Law of Atmospheres
	11.2. PASCAL’S PRINCIPLE
	11.3. ARCHIMEDES’ PRINCIPLE
	11.4. BERNOULLI’S EQUATION
CHAPTER 12: Thermodynamics
	12.1. TEMPERATURE
	12.2. HEAT
		12.2.1. Conduction
		12.2.2. Convection
		12.2.3. Radiation
	12.3. BOLTZMANN CONSTANT
	12.4. IDEAL GAS LAW
	12.5. HEAT CAPACITY
	12.6. FIRST LAW
		12.6.1. Constant Volume
		12.6.2. Constant Pressure
		12.6.3. Constant Temperature
		12.6.4. Adiabatic
	12.7. ENTROPY
	12.8. SECOND LAW
CHAPTER 13: Waves
	13.1. WAVE EQUATION
	13.2. TRAVELING WAVES
	13.3. GROUP AND PHASE VELOCITY
	13.4. STANDING WAVES
	13.5. WAVE ON A STRING
	13.6. POWER
	13.7. SOUND WAVES
		13.7.1. Speed of Sound Waves
		13.7.2. Wave Form
		13.7.3. Intensity
		13.7.4. Doppler Effect
	13.8. LIGHT WAVES
	13.9. FOURIER SERIES
APPENDIX A: Mathematica Starter
	A.1. Input and Text Cells
	A.2. Palettes
	A.3. Cell Display
	A.4. Introduction to Functions
	A.5. User Defined Function
	A.6. Reserved Names
	A.7. Units
	A.8. Natural Language Box
	A.9. Physical constants and their units
	A.10. Calculations with units
	A.11. Solving equations
	A.12. Series expansion
	A.13. Taking a Limit
	A.14. Derivatives
	A.15. Integrals
	A.16. Drawing objects
	A.17. Plotting
APPENDIX B: Spherical and Cylindrical Coordinates
	B.1. Spherical Coordinates
	B.2. Cylindrical Coordinates
Index