Newtonian Mechanics [First ed.] 9780393099706

Table of contents :
Front Cover
The M.I.T. Introductory Physics Series
Full Title Page
Copyright
Contents
Preface
Newtonian mechanics
Prologue
EXERCISES-HORS D'OEUVRES
Part I The approach to Newtonian dynamics
1 A universe of particles
THE PARTICULATE VIEW
ELECTRONS AND NUCLEONS
ATOMIC NUCLEI
ATOMS
MOLECULES: LIVING CELLS
SAND AND DUST
OTHER TERRESTRIAL OBJECTS
PLANETS AND SATELLITES
STARS
GALAXIES
PROBLEMS
2 Space, time, and motion
WHAT IS MOTION?
FRAMES OF REFERENCE
COORDINATE SYSTEMS
COMBINATION OF VECTOR DISPLACEMENTS
THE RESOLUTION OF VECTORS
VECTOR ADDITION AND THE PROPERTIES OF SPACE
TIME
UNITS AND STANDARDS OF LENGTH AND TIME
Length
Time
SPACE-TIME GRAPHS
VELOCITY
INSTANTANEOUS VELOCITY
RELATIVE VELOCITY AND RELATIVE MOTION
PLANETARY MOTIONS: PTOLEMY VERSUS COPERNICUS
PROBLEMS
3 Accelerated motions
ACCELERATION
THE ANALYSIS OF STRAIGHT-LINE MOTION
A COMMENT ON EXTRANEOUS ROOTS
TRAJECTORY PROBLEMS IN TWO DIMENSIONS
FREE FALL OF INDIVIDUAL ATOMS
OTHER FEATURES OF MOTION IN FREE FALL
UNIFORM CIRCULAR MOTION
VELOCITY AND ACCELERATION IN POLAR COORDINATES
PROBLEMS
4 Forces and equilibrium
FORCES IN STATIC EQUILIBRIUM
UNITS OF FORCE
EQUILIBRIUM CONDITIONS; FORCES AS VECTORS
ACTION AND REACTION IN THE CONTACT OF OBJECTS
ROTATIONAL EQUILIBRIUM; TORQUE
FORCES WITHOUT CONTACT; WEIGHT
PULLEYS AND STRINGS
PROBLEMS
5 The various forces of nature
THE BASIC TYPES OF FORCES
GRAVITATIONAL FORCES
ELECTRIC AND MAGNETIC FORCES
NUCLEAR FORCES
FORCES BETWEEN NEUTRAL ATOMS
CONTACT FORCES
FRICTIONAL CONTACT FORCES
CONCLUDING REMARKS
PROBLEMS
6 Force, inertia, and motion
THE PRINCIPLE OF INERTIA
FORCE AND INERTIAL MASS: NEWTON'S LAW
SOME COMMENTS ON NEWTON'S LAW
SCALES OF MASS AND FORCE
THE EFFECT OF A CONTINUING FORCE
THE INVARIANCE OF NEWTON'S LAW; RELATIVITY
INVARIANCE WITH SPECIFIC FORCE LAWS
NEWTON'S LAW AND TIME REVERSAL
CONCLUDING REMARKS
PROBLEMS
Part II Classical mechanics at work
7 Using Newton's law
MOTION IN TWO DIMENSIONS
MOTION IN A CIRCLE
CURVILINEAR MOTION WITH CHANGING SPEED
CIRCULAR PATHS OF CHARGED PARTICLES IN UNIFORM MAGNETIC FIELDS
CHARGED PARTICLE IN A MAGNETIC FIELD
MASS SPECTROGRAPHS
THE FRACTURE OF RAPIDLY ROTATING OBJECTS
MOTION AGAINST RESISTIVE FORCES
DETAILED ANALYSIS OF RESISTED MOTION
MOTION GOVERNED BY VISCOSITY
GROWTH AND DECAY OF RESISTED MOTION
AIR RESISTANCE AND "INDEPENDENCE OF MOTIONS"
SIMPLE HARMONIC MOTION
MORE ABOUT SIMPLE HARMONIC MOTION
Fitting the initial conditions
Dynamical relation between SHM and circular motion
PROBLEMS
8 Universal gravitation
THE DISCOVERY OF UNIVERSAL GRAVITATION
THE ORBITS OF THE PLANETS
PLANETARY PERIODS
KEPLER'S THIRD LAW
THE MOON AND THE APPLE
FINDING THE DISTANCE TO THE MOON
The earth's radius
Modern methods
THE GRAVITATIONAL ATTRACTION OF A LARGE SPHERE
OTHER SATELLITES OF THE EARTH
THE VALUE OF G, AND THE MASS OF THE EARTH
LOCAL VARIATIONS OF g
THE MASS OF THE SUN
FINDING THE DISTANCE TO THE SUN
MASS AND WEIGHT
WEIGHTLESSNESS
LEARNIN G ABOUT OTHER PLANETS
The moons of Jupiter
THE DISCOVERY OF NEPTUNE
GRAVITATION OUTSIDE THE SOLAR SYSTEM
EINSTEIN'S THEORY OF GRAVITATION
PROBLEMS
9 Collisions and conservation laws
THE LAWS OF IMPACT
THE CONSERVATION OF LINEAR MOMENTUM
MOMENTUM AS A VECTOR QUANTITY
ACTION, REACTION, AND IMPULS E
EXTENDING THE PRINCIPLE OF MOMENTUM CONSERVATION
THE FORCE EXERTED BY A STREAM OF PARTICLES
REACTION FROM A FLUID JET
ROCKET PROPULSION
COLLISION S AND FRAMES OF REFERENCE
KINETIC ENERGY IN COLLISIONS
THE ZERO-MOMENTUM FRAME
COLLISION PROCESSES IN TWO DIMENSIONS
ELASTIC NUCLEAR COLLISIONS
IN ELASTIC AND EXPLOSIVE PROCESSES
WHAT IS A COLLISION?
INTERACTING PARTICLES SUBJECT TO EXTERNAL FORCES
THE PRESSURE OF A GAS
THE NEUTRINO
PROBLEMS
10 Energy conservation in dynamics; vibrational motions
INTRODUCTION
INTEGRALS OF MOTION
WORK, ENERGY, AND POWER
GRAVITATIONAL POTENTIAL ENERGY
MORE ABOUT ONE-DIMENSIONAL SITUATIONS
THE ENERGY METHOD FOR ONE-DIMENSIONAL MOTIONS
SOME EXAMPLES OF THE ENERGY METHOD
Bouncing ball
Mass on a spring
Dynamics of a catapult
SMALL OSCILLATIONS IN GENERAL
THE LINEAR OSCILLATOR AS A TWO-BODY PROBLEM
COLLISION PROCESSES INVOLVING ENERGY STORAGE
THE DIATOMIC MOLECULE
The molecular spring constant
The molecular vibrations
PROBLEMS
11 Conservative forces and motion in space
EXTENDING THE CONCEPT OF CONSERVATIVE FORCES
ACCELERATION OF TWO CONNECTED MASSES
OBJECT MOVING IN A VERTICAL ClRCLE
AN EXPERIMENT BY GALILEO
MASS ON A PARABOLIC TRACK
THE SIMPLE PENDULUM
THE PENDULUM AS A HARMONIC OSCILLATOR
Linear motion
Angular motion
THE PENDULUM WITH LARGER AMPLITUDE
UNIVERSAL GRAVITATION: A CONSERVATIVE CENTRAL FORCE
A GRAVITATING SPHERICAL SHELL
A GRAVITATING SPHERE
ESCAPE VELOCITIES
MORE ABOUT THE CRITERIA FOR CONSERVATIVE FORCES
FIELDS
EQUIPOTENTIAL SURFACES AND THE GRADIENT OF POTENTIAL ENERGY
MOTION IN CONSERVATIVE FIELDS
THE EFFECT OF DISSIPATIVE FORCES
GAUSS'S LAW
APPLICATIONS OF GAUSS'S THEOREM
Field outside a sphere
Field inside a sphere
Field due to a flat sheet
PROBLEMS
Part III Some special topics
12 Inertial forces and noninertial frames
MOTION OBSERVED FROM UNACCELERATED FRAMES
MOTION OBSERVED FROM AN ACCELERATED FRAME
ACCELERATED FRAMES AND INERTIAL FORCES
ACCELEROMETERS
ACCELERATING FRAMES AND GRAVITY
CENTRIFUGAL FORCE
CENTRIFUGES
CORIOLIS FORCES
DYNAMICS ON A MERRY-GO-ROUND
GENERAL EQUATION OF MOTION IN A ROTATING FRAME
THE EARTH AS A ROTATING REFERENCE FRAME
Deviation of freely falling objects
Patterns of atmospheric circulation
The Foucault pendulum
THE TIDES
TIDAL HEIGHTS; EFFECT OF THE SUN
THE SEARCH FOR A FUNDAMENTAL INERTIAL FRAME
SPECULATIONS ON THE ORIGIN OF INERTIA
PROBLEMS
13 Motion under central forces
BASIC FEATURES OF THE PROBLEM
THE LAW OF EQUAL AREAS
THE CONSERVATION OF ANGULAR MOMENTUM
ENERGY CONSERVATION IN CENTRAL FORCE MOTIONS
USE OF THE EFFECTIVE POTENTIAL-ENERGY CURVES
BOUNDED ORBITS
UNBOUNDED ORBITS
CIRCULAR ORBITS IN AN INVERSE-SQUARE FORCE FIELD
SMALL PERTURBATION OF A CIRCULAR ORBIT
THE ELLIPTIC ORBITS OF THE PLANETS
DEDUCING THE INVERSE-SQUARE LAW FROM THE ELLIPSE
ELLIPTIC ORBITS: ANALYTICAL TREATMENT
ENERGY IN AN ELLIPTIC ORBIT
MOTION NEAR THE EARTH'S SURFACE
INTERPLANETARY TRANSFER ORBITS
CALCULATING AND ORBIT FROM INITIAL CONDITIONS
A FAMILY OF RELATED ORBITS
CENTRAL FORCE MOTION AS A TWO-BODY PROBLEM
DEDUCING THE ORBIT FROM THE FORCE LAW
RUTHERFORD SCATTERING
CROSS SECTIONS FOR SCATIERING
AN HISTORICAL NOTE
PROBLEMS
14 Extended systems and rotational dynamics
MOMENTUM AND KINETIC ENERGY OF A MANY-PARTICLE SYSTEM
ANGULAR MOMENTUM
ANGULAR MOMENTUM AS A FUNDAMENTAL QUANTITY
CONSERVATION OF ANGULAR MOMENTUM
MOMENTS OF INERTIA OF EXTENDED OBJECTS
Special cases
1. Uniform ring
2. Uniform disk
3. Uniform Bar
TWO THEOREMS CONCERNING MOMENTS OF INERTIA
Theorem of perpendicular axes
KINETIC ENERGY OF ROTATING OBJECTS
ANGULAR MOMENTUM CONSERVATION AND KINETIC ENERGY
TORSIONAL OSCILLATIONS AND RIGID PENDULUMS
MOTION UNDER COMBINED FORCES AND TORQUES
IMPULSIVE FORCES AND TORQUES
BACKGROUND TO GYROSCOPIC MOTION
GYROSCOPE IN STEADY PRECESSION
MORE ABOUT PRECESSIONAL MOTION
GYROSCOPES IN NAVIGATION
ATOMS AND NUCLEI AS GYROSCOPES
GYROSCOPIC MOTION IN TERMS OF F = ma
NUTATION
Formal analysis
THE PRECESSION OF THE EQUINOXES
PROBLEMS
Appendix
THE METRIC SYSTEM OF UNITS
CONVERSION FACTORS
GENERAL CONSTANTS
Bibliography
SOME CLASSIC WORKS
BIOGRAPHIES
HISTORICAL OR PHILOSOPHICAL IN EMPHASIS
ASTRONOMICAL
SOME GENERAL TEXTBOOKS
MECHANICS TEXTS
ENGINEERING MECHANICS
INDIVIDUAL TOPICS
Answers to problems
Index
Back Flap
Back Cover

Citation preview

ewton1an mechanic A.P. French

The M.I.T. Introductory Physics Series

A.P. FRENCH

Special RelatiVti y

A.P. FRENCH

Vibrations and Waves

A.P. FRENCH

Newtonian Mechanics

The M.I.T. Introductory Physics Series

Newtonian Mechanics A.P. French

PROFESSOR OP MATHEMATICS, THE MASSACHUSETTS INSTITUTE OP TECHNOLOGY

Nelson

THOMAS NELSON AND SONS LTD

36 Park Street London wl Y 4o£ 18123 Nairobi Kenya·

PO Box

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Street Melbourne 3000 THOMAS NELSON A"-"D SONS (CANADA) LTD 81 Curlew Drive Don Mills Ontario 597 Little Collins

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THOMAS NELSOS (NIGERIA) LTD

Box 336 Apapa Lagos SONS (SOUTH AFRICA) (PROPRIETARY) LTD 51 Commissioner Street Johannesburg

THOMAS NELSON AND

Copyright © 1971, 1965 by the Massachusetts Institute of Technology First published in Great Britain 1971

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SBN 17 771074 8 (paper) 17 761075

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Made and printed by William Clowes & Sons Ltd, Beccles, Colchester and London

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Preface Prologue

PART I

1

xi 3

THE APPROACH TO NEWTONIAN DYNAMICS

A universe of particles

The particulate view 2I Electrons and nucleons 24 Atomic nuclei 25 26 Atoms 28 Molecules; living cells Sand and dust 31 Other terrestrial objects 32 Planets and satellites 33 Stars 35 Galaxies 36 PROBLEMS

'

21

38

Space, time, and motion

43

What is motion? 43 Frames of reference 46 Coordinate systems 48 v

53 Combination of i;ector displacements The resolution of vectors 56 59 Vector addition and the properties of space Time 61 63 Units and standards of length and time 66 Space-time graphs 67 Velocity 68 Instantaneous velocity Relative velocity and relatiL'e motion 72 74 Planetary motions: Ptolemy versus Copernicus PROBLEMS

3

78

85

Accelerated motions 85 Acceleration Tlte analysis of straight-line motion 87 A comment on extraneous roots 93 95 Trajectory problems in t1110 dimensions Free fall of individual atoms 98 Other features of motion in free fall 102 Uniform circular motion /05 Velocity and acceleration in polar coordinates PROBLEMS

4

106

/08

115

Forces and equilibrium 1 16 Forces in static equilibrium Units offorce 1 18 1 19 Equilibrium conditions; forces as vectors Action and reaction in the contact of objects 123 124 Rotational equilibrium; torque 128 Forces 111ithout contact; 111eight Pulleys and strings 130 PROBLEMS

5

/32

The various forces of nature

Tlte basic types of forces I39 140 Gravitational forces 145 Electric and magnetic forces 147 Nuclear forces 148 Forces bet111een neutral atoms Contact forces 150 Frictional contact forces 152 154 Concluding remarks PROBLEMS

vi

154

139

6

Force, inertia, and motion

161

The principle of inertia 161 and inertial mass: Newton's law 164 167 Same comments on Newton's law Scales of mass and force 170 The effect of a continuing force 173 173 The invariance of Newton's law; relativity Invariance with specific force laws 176 Newton's law and time reversal 178 Concluding remarks 180 18/ PROBLEMS Force

PART II

7

CLASSICAL M ECHAN ICS AT WORK

Using Newton's law

Some introductory examples 188 Motion in two dimensions 194 Motion in a circle 198 Curvilinear motion with changing speed 200 Circular paths of charged particles in uniform magnetic fields Clwrged particle in a magnetic field 205 Muss spectrographs 206 208 The fracture of rapidly rotating objects Motion against resistive forces 2/ 0 Detailed analysis of resisted motion 2I 3 Motion goi:erned by viscosity 218 Growth and decay of resisted motion 221 225 Air resistance and "independence of motions" Simple harmonic motion 226 231 More about simple harmonic motion 234 PROBLEMS 8

Universal gravitation

245 The discoi:ery of unii:ersa/ gravitation The orbits of the planets 246 249 Planetary periods Kepler's third Jaw 252 The moon and the apple 256 259 Finding the distance to the moon 261 The gravitalional a11rac1ion of a large sphere Other satellites of 1he earlh 265 268 The value of G, and 1he mass of the earth Local variations of g 270 The mass of the sun 274 vii

187

202

245

279

Finding 1he distance to the sun Mass and weight

Learning abotlJ other planets

275

285

Weigh1/essness

The moons of Jupi1er

291

288

The discovery of Neptune

286 299

Gravi1a1ion outside the solar system

JO/

Einstein's theory of graoitation PROBLEMS

9

295

307

Collisions and conservation laws The laws of impact

308

The conservation of linear momentum Momentum as a vector quantity

309

310 313

Action, reaction, and impulse

Extending the prindple of momentum conservation The force exerted by a stream of particles Reaction from a fluid jet Rocket propulsion

324

327

Collisions and frames of reference

331

333 335

Kinetic energy in collisions The zero-momentum frame

Collision processes in two dimensions Inelastic and explosii:e processes Elastic nuclear collisions What is a collision?

339

342 346

351

Interacting particles subject to externol forces PROBLEMS

I0

352

354

The pressure of a gas The neutrino

318

321

356 157

Energy conservation in dynamics; 367

vibrational motions Introduction

367

Integrals of motion

368

Work, energy, and power

373

Gravitational potential energy

376

More about one-dimensional sitlllltions

379 381

The energy method for one-dimensional motions Some examples of the energy method

384

The harmonic oscillator by the energy method Small oscillations in general

395

The linear oscillator as a two-body prob/em Collision proceSMs involving energy storage The diatomic molecule PROBLEMS

viii

41/

405

393 400

397

I I

Conservative forces and motion in space

Extending the concept of conservative forces 423 Acceleration of tll'o connected masses 425 426 Object moving in a vertical circle 429 An experiment b.v Galileo Mass on a parabolic track 431 The simple pendulum 434 437 The pendulum as a harmonic oscillator The pendulum with larger amplitude 440 442 Universal graviwtion: a conservative central force 446 A gravitating spherical shell A gravitating sphere 450 Escape i:elocitirs 453 457 More about the criteria jar conservative forces Fields 461 E:Quipotential surfaces and the gradient of potential energy Motion in conservative fields 466 The effect of dissipative forces 470 473 Gauss's /all' 476 Applications of Gauss's theorem PART III

I2

PROBLEMS

423

463

478

SOME SPECIAL TOPICS

Inertial forces and non-inertial frames

493

Motion observed from unaccelerated frames 494 Motion obser1:ed from an accelerated frame 495 Accelerated frames and inertial forces 497 501 Accelerometers 504 Accelerating frames and gravity Cen"ifuga/ j(Jrce 507 511 Centrifuges 514 Coriolis forces Dynamics on a merry-go-round 518 519 General equation of motion in a rotating frame The earth as a rotating reference frame 524 531 The tides Tidal heights; efef ct of the sun 535 538 The search for a fundamental inertial frame Speculations on the origin of inertia 542 PROBLEMS

13

546

Motion under central forces 555 Basic features of the problem The law of equal areas 557 The consercation of angular momentum

ix

555

560

Energ)1 conservation in central force motions 563 Use