Huggins Dartmouth College physics2000.com MKS Units (link to CGS Units) m = meters kg = kilograms s = seconds N = newtons J = joules C = coulombs T = tesla F = farads H = henrys Powers of 10 A = amperes K = kelvins mol = mole Power Prefix Symbol speed of light c 3.00 × 10 8 m / s 10 12 tera T gravitational constant G 6.67 × 10 –11N⋅m2 / kg 2 10 9 giga G permittivity constant ε0 8.85 × 10 – 12F / m 10 6 mega M permeability constant µ0 1.26 × 10 –6 H/m 10 3 kilo k elementary charge e 1.60 × 10 –19 C 10 2 hecto h electron volt eV 1.60 × 10 –19 J 10 – 1 deci d electron rest mass me 9.11 × 10 – 31 kg 10 – 2 centi c proton rest mass mp 1.67 × 10 – 27 kg 10 – 3 milli m Planck constant h 6.63 × 10 – 34 J⋅ s 10 – 6 micro µ Planck constant / 2 π h 1.06 × 10 – 34 J⋅ s 10 – 9 nano n Bohr radius rb 5.29 × 10 – 11m 10 – 12 pico p 10 – 15 femto f Bohr magneton µb 9.38 × 10 –23J / K Avogadro constant NA 6.02 × 10 23mol – 1 universal gas constant R 8.31 J /mol⋅ K Dimensions Quantity Unit Equivalents Force newton N J/m kg •m/ s2 Energy joule J N• m kg • m2/s2 2 3 Power watt W J/s kg • m /s 2 Pressure pascal Pa N/m 2 kg/m• s Frequency hertz Hz cycle/s s–1 Electric charge coulomb C A•s Electric potential volt V J/C kg • m2/A • s3 Ω 2 2 3 Electric resistance ohm V/A kg • m /A • s 2 4 2 Capacitance farad F C/V A • s /kg • m 2 Magnetic field tesla T N • s/C • m kg/A • s 2 2 2 Magnetic flux weber Wb T• m kg • m /A• s Inductance henry H V• s/A kg • m2/A2• s2 Copyright © 2000 Moose Mountain Digital Press Etna, New Hampshire 03750 All rights reserved www.com Preface & TOC-i Physics2000 Student project by Bob Piela explaining the hydrogen molecule ion. Huggins Department of Physics Dartmouth College Hanover, New Hampshire i www.com Preface & TOC-iii Preface ABOUT THE COURSE Most students experience difficulty when they first Physics2000 is a calculus based, college level introduc- encounter abstract concepts like vector fields and Gauss’ tory physics course that is designed to include twentieth law. To provide a familiar model for a vector field, we century physics throughout. This is made possible by begin the section on electricity and magnetism with a introducing Einstein’s special theory of relativity in the chapter on fluid dynamics.
It is easy to visualize the first chapter. This way, students start off with a modern velocity field of a fluid, and Gauss’ law is simply the picture of how space and time behave, and are prepared statement that the fluid is incompressible. We then show to approach topics such as mass and energy from a that the electric field has mathematical properties simi- modern point of view. lar to those of the velocity field.
The course, which was developed during 30 plus years The format of the standard calculus based introductory working with premedical students, makes very gentle physics text is to put a chapter on special relativity assumptions about the student’s mathematical back- following Maxwell’s equations, and then put modern ground. All the calculus needed for studying Phys- physics after that, usually in an extended edition. This ics2000 is contained in a supplementary chapter which format suggests that the mathematics required to under- is the first chapter of a physics based calculus text. We stand special relativity may be even more difficult than can cover all the necessary calculus in one reasonable the integral-differential equations encountered in length chapter because the concepts are introduced in Maxwell’s theory.
Such fears are enhanced by the the physics text and the calculus text only needs to strangeness of the concepts in special relativity, and are handle the formalism. (The remaining chapters of the driven home by the fact that relativity appears at the end calculus text introduce the mathematical tools and con- of the course where there is no time to comprehend it. cepts used in advanced introductory courses for physics This format is a disaster. and engineering majors.
These chapters will appear on Special relativity does involve strange ideas, but the a later version of the Physics2000 CD, hopefully next mathematics required is only the Pythagorean theorem.) By placing relativity at the beginning of the course you In the physics text, the concepts of velocity and accelera- let the students know that the mathematics is not diffi- tion are introduced through the use of strobe photo- cult, and that there will be plenty of time to become graphs in Chapter 3. How these definitions can be used familiar with the strange ideas. By the time students to predict motion is discussed in Chapter 4 on calculus have gone through Maxwell’s equations in Physics2000, and Chapter 5 on the use of the computer. they are thoroughly familiar with special relativity, and are well prepared to study the particle-wave nature of Students themselves have made major contributions to matter and the foundations of quantum mechanics.
This the organization and content of the text. Student’s material is not in an extended edition because there is of enthusiasm for the use of Fourier analysis to study time to cover it in a comfortably paced course. musical instruments led to the development of the MacScope™ program. The program makes it easy to use Fourier analysis to study such topics as the normal modes of a coupled aircart system and how the energy- time form of the uncertainty principle arises from the particle-wave nature of matter.com Preface & TOC-iv ABOUT THE PHYSICS2000 CD ABOUT THE AUTHOR The Physics2000 CD contains the complete Physics2000 E.
Huggins has taught physics at Dartmouth College text in Acrobat™ form along with a supplementary since 1961. He was an undergraduate at MIT and got his chapter covering all the calculus needed for the text. thesis under Richard Included on the CD is a motion picture on the time Feynman was on aspects of the quantum theory of dilation of the Muon lifetime, and short movie segments gravity and the non uniqueness of energy momentum of various physics demonstrations. Also a short cook- tensors.
Since then most of his research has been on book on several basic dishes of Caribbean cooking. The superfluid dynamics and the development of new teach- CD is available at the web site ing tools like the student built electron gun and MacScope™. He wrote the non calculus introductory www.com physics text Physics1 in 1968 and the computer based text Graphical Mechanics in 1973. The Physics2000 The cost is $10.
text, which summarizes over thirty years of experiment- Also available is a black and white printed copy of the ing with ways to teach physics, was written and class text, including the calculus chapter and the CD, at a cost tested over the period from 1990 to 1998. All the work of $ 39 plus shipping. of producing the text was done by the author, and his wife, Anne Huggins. The text layout and design was The supplementary calculus chapter is the first chapter done by the author’s daughter Cleo Huggins who de- of a physics based calculus text which will appear on a signed eWorld™ for Apple Computer and the Sonata™ later edition of the Physics2000 CD.
As the chapters are music font for Adobe Systems. ready, they will be made available on the web site. The author’s eMail address is Use of the Text Material lish.edu Because we are trying to change the way physics is taught, Chapter 1 on special relativity, although copy- The author is glad to receive any comments. righted, may be used freely (except for the copyrighted photograph of Andromeda and frame of the muon film).
All chapters may be printed and distributed to a class on a non profit basis.com Preface & TOC-i Table of Contents PART 1 CHAPTER 1 PRINCIPLE OF RELATIVITY Front Cover MKS Units. Front cover-2 The Principle of Relativity. Front cover-2 A Thought Experiment. Front cover-2 Statement of the Principle of Relativity.
1-4 Basic Law of Physics. 1-6 Preface Measurement of the Speed of Waves. 1-7 About the Course. iii Michaelson-Morley Experiment.
1-11 About the Physics2000 CD. iv Einstein’s Principle of Relativity. 1-12 Use of the Text Material. iv The Special Theory of Relativity.
1-13 About the Author. iv Moving Clocks. 1-18 INTRODUCTION—AN OVERVIEW OF PHYSICS Real Clocks. 1-20 Space And Time.
int-2 Time Dilation. 1-22 The Expanding Universe. int-3 Space Travel. 1-22 The Lorentz Contraction.
1-24 Structure of Matter. int-5 Relativistic Calculations. int-5 Approximation Formulas. int-8 A Consistent Theory.
1-32 The Bohr Model. int-8 Lack of Simultaneity. 1-32 Particle-Wave Nature of Matter. 1-36 Conservation of Energy.
int-12 Class Handout. 1-39 Particle Nature of Forces. int-14 CHAPTER 2 VECTORS Gravity. int-16 Displacement Vectors.
int-17 Arithmetic of Vectors. int-19 Rules for Number Arithmetic. 2-4 The Weak Interaction. int-20 Rules for Vector Arithmetic.
int-21 Multiplication of a Vector by a Number. int-22 Magnitude of a Vector. int-22 Graphical Work. 2-8 The Electroweak Theory.
int-26 Vector Equations in Component Form. 2-10 The Early Universe. int-27 Vector Multiplication. 2-11 The Thermal Photons.
int-29 The Scalar or Dot Product. 2-12 Interpretation of the Dot Product. 2-14 Vector Cross Product. 2-15 Magnitude of the Cross Product.
2-17 Component Formula for the Cross Product. 2-17 Right Handed Coordinate System .com Preface & TOC-ii CHAPTER 3 DESCRIPTION OF MOTION CHAPTER 5 COMPUTER PREDICTION OF Displacement Vectors. 3-5 MOTION A Coordinate System. 3-7 Step-By-Step Calculations.
5-2 Manipulation of Vectors. 3-8 Calculating and Plotting a Circle. 5-2 Measuring the Length of a Vector. 3-9 Program for Calculation.
5-4 Coordinate System and Coordinate Vectors. 3-11 The DO LOOP. 5-4 Analysis of Strobe Photographs. 3-11 The LET Statement.
5-6 Determining Acceleration Plotting a Point. 5-6 from a Strobe Photograph. 5-7 The Acceleration Vector. 5-8 Uniform Circular Motion.
5-10 Magnitude of the Acceleration for Circular Motion 3-18 Prediction of Motion. 5-12 An Intuitive Discussion of Acceleration. 3-20 Time Step and Initial Conditions. 5-14 Acceleration Due to Gravity.
3-21 An English Program for Projectile Motion. 5-16 Projectile Motion with Air Resistance. 3-22 A BASIC Program for Projectile Motion. 3-24 Projectile Motion with Air Resistance.
5-22 Instantaneous Velocity from a Strobe Photograph 3-26 Air Resistance Program. 5-24 CHAPTER 4 CALCULUS IN PHYSICS CHAPTER 6 MASS Limiting Process. 4-1 Definition of Mass. 6-2 The Uncertainty Principle.
6-2 Calculus Definition of Velocity. 4-3 Properties of Mass. 4-6 Addition of Mass. 6-4 Distance, Velocity and A Simpler Way to Measure Mass.
6-4 Acceleration versus Time Graphs. 4-7 Inertial and Gravitational Mass. 6-5 The Constant Acceleration Formulas. 4-9 Mass of a Moving Object.
6-6 Projectile Motion with Air Resistance. 4-14 Electron Mass in β Decay. 6-7 Solving the Differential Equation. 6-8 Solving Projectile Motion Problems.
4-19 The Einstein Mass Formula. 6-10 Nature’s Speed Limit. 6-11 Zero Rest Mass Particles .com Preface & TOC-iii CHAPTER 7 CONSERVATION OF LINEAR & CHAPTER 9 APPLICATIONS OF NEWTON’S ANGULAR MOMENTUM SECOND LAW Conservation of Linear Momentum. 7- 2 Addition of Forces.
7- 7 The Spring Pendulum .