Table Of Content

• o o - •" "o o o • W • E , o > • •• I . • , Table of Values • Symbol or Derivation Value and Units Item Abbreviation of Value General 57.3°(5r 18') 1 radian rad 180°/'IT 3.44 X 103 minutes (of arc) 1 radian rad 2.06 X 105 seconds (of arc) = 1 radian rad 1.75 X 10-2 rad 1 degree 'IT/180° 2.91 X 10-4 rad = 1 minute (of arc) 4.85 X 10-6 rad 1 second (of arc) • 1.609 X 105 cm 1 statute mile 10-8 cm = 1 angstrom A 10-4 cm - 1 micrometer (micron) J-lm 2.998 X 102 V = 1 statvolt 10-8 C 2.99725 X 1010 cm/s Speed of light in vacuum C ; 6:::.:697810 Xcm1/0s-28 dyn-cm2/g2 GAcracevilteartaiotinoanl ocfongsratavnitty at earth's surface g GMe/Re2 6.671 X 10-11 N-m2/kg 2 Gravitational constant }G 1 dyne =1 g-cm/s2 dyn • 1 newton - 1 kg-m/s2 N Astronomical 3.084 X 1018 cm parsec 9.464 X 1017 cm light year c X s/yr 1.49 X 1013 cm astronomical unit (_ radius of earth's orbit) AU ;:::: 1080 Number of nucleons ;:::: 1028 cm Radius ;:::: 1011 Number of galaxies ) Koowo uo;v"", ;:::: 1.6 X 10-18 (cm/s)/cm Speed of recession of nebulae ;::::1.6 X 1011 Number of stars ; ;: 810X23 1cm044 9 DMiasmseter 1G,I", 6.96 X 1010 cm Radius 2 1.1949 X 10633s9 PMearsiosd of rotation 1Suo 1.49 X 1013 cm Radius of orbit 6.37 X 108 cm Mean radius 5.98 X 1027 9 Mass 5.52 g/cm3 Mean density Earth 3.156Xl07 s = 1 year (period of revolution) 8.64 X 104 s = 24 hours (period of rotation) 3.84 X 1010 cm Radius of orbit 1.74Xl08 cm Radius 7.34 X 1025 9 Mass ) Moo~ 2.36 X 106 s Period of revolution / - J::* Table of Vall 1 Value and Units Item Abbr~lIla~.. Gases 62.206.9242X2 X103190cc2m3m"3m/-m3ool-l1 AMLovosolcagharmdvroiodl'uts'smnenuumamtbbSeeTrrP nNVo No/Vo 8.314 X 107 ergs mol-1 deg-1 Gas constant R 1.381 X 10-16 erg/K Boltzmann's constant k R/N 1.01 X 106 dyn/cm2 Atmospheric pressure :; 10-5 cm Mean free path at STP 3.32 X 104 cm/s Speed of sound in air at STP Atomic 6.62~2 X 10-27 erg-s Planck's constant h 1.0546 X 10-27 erg-s Planck's constant/2?T 11 h/'2?T 13.6 electron volts Energy associated with 1 Rydberg Ry 1.6022 X 10-12 erg Energy associated with 1 electron volt eV 1.2398 X 10-4 cm Wavelength associated with 1 electron volt 2.4180 X 1014 S-l Frequency associated with 1 electron volt 0.5292 X 10-8 cm Bohr radius of the ground state of hydrogen :; 10-8 cm Radius of an atom 0.9274 X 10-20 erg/G Bohr magneton eY1/2mc 137.036 Reciprocal of fine-structure constant 11c/e2 Particles 1.67265 X H>-24 g Proton rest mass 1.67496 X 10-24 g Neutron rest mass 1.66057 X 10-24 g 1 unified atomic mass unit ( n mass of C12) 0.910954 X 10-27 g Electron rest mass 0.93828 X 109 eV Energy equivalent to proton rest mass 0.511004 X 106 eV Energy equivalent to electron rest mass 0.93150 X 109 eV Energy equivalent to 1 atomic mass unit 1836 Proton mass/electron mass 2.818 X 10-13 cm Classical radius of the electron 4.80325 X 10-10 esu Charge on proton 1.60219 X 10-19 C Charge on proton 2.423 X 10-10 cm Electron Compton wavelength h/mc / l- I • \ I I--__----------.----............--=::-::=::-~~~___.I....._ • Mechanics • Charles Kittel Professor of Physics University of California Berkeley Walter D. Knight Professor of Physics University of California Berkeley Malvin A. Ruderman Professor of Physics New York University • Revised by A. Carl Helmholz Professor of Physics University of California Berkeley Burton J. Moyer Dean of the College of Liberal Arts University of Oregon Eugene McGRAW-HILL BOOK COMPANY New York St. Louis San Francisco Dusseldorf Johannesburg. Kuala Lumpur London Mexico Montreal New Delhi Panama Rio de Janeiro Singapore Sydney Toronto Mechanics -530 -~',..._~~. _•.. " ...,..,..,..".",.... ~,f'.c.. vol·1 53\ B.P IIIIIIIIIII~ 5084 Berkeley Physfcs-COurse Volume 1, Second Edition This book was set In Laurel by York Graphic Services, Inc. The editors were Jack L. Farnsworth, Eva Marie Strock, and Ida Abrams Wolfson; the designer was Michael A Rogondino; and the production super- visor was Adam Jacobs The drawings were done by Ayxa Art. The printer was Halliday Lithograph Corporation Front cover NGC 4594 spiral galaxy in Virgo, seen on edge; 200-1n photograph The dark band IS due to absorption by a nng of matter surrounding the bnght central core (Photograph courtesy of the Hale Observatories) Back cover Hydrogen bubble chamber picture of the production of an anti-Z In the reaction K+ + P (Photograph courtesy of the Lawrence Berkeley Laboratory) MECHANICS Copyright © 1973 by McGraw-Hili, Inc. All rights reserved. Pnnted In the United States of America No part of this publication may be reproduced, stored In a retrieval system, or transmitted, In any form or by any means, electronic, mechanical, photocopying, recording, or otherWise, without the pnor wntten permission of the publisher Library of Congress Cataloging in Publication Data Kittel, Charles Mechanics (Berkeley physIcs course, v 1) 1 Mechanics I. Knight. Walter D, JOint author, II Ruderman, MalVin A, JOint author. III Helmholz, A Carl, ed IV. Moyer, Burton J, ed V Title. VI Senes OC1B375 vol 1 [OC1252] 530'08s [531] 72-7444 ISBN 0-07-004880-0 6 7 8 9 10 HDHD 8543210 The first edition of the Berkeley PhysIcs Course MECHANICS, Vol. 1 copyright © 1963, 1964, 1965 by Educational Development Center was supported by a grant from the National Science Founda- tion to EDC This matenal IS available to publishers and authors on a royalty-free baSIS by applYing to the Educational Development Center Foreword VI Preface to the Second Edition of Volume 1 vii Original Preface to the Berkeley Physics Course IX Teaching Notes xi Note to the Student xvi Notation xvii Introd uction 2 2 Vectors 26 3 Newton's Laws of Motion 56 4 Frames of Reference: Galilean Transformation 100 5 Conservation of Energy 134 6 Conservation of Linear and Angular Momentum 172 7 Harmonic Oscillator: Properties and Examples 200 8 Elementary Dynamics of Rigid Bodies 238 9 Inverse-square-Iaw Force 268 10 The Speed of Light 298 11 Special Relativity: The Lorentz Transformation 324 12 Relativistic Dynamics: Momentum and Energy 348 13 Problems in Relativistic Dynamics 374 14 Principle of Equivalence 396 Appendix 410 Film Lists 411 Index 415 Contents One of the urgent problems confronting universities today is that of undergraduate teaching. As research has become more and more absorbing to the faculty, a "subtle discounting of the teaching process" (to quote phi- losopher Sidney Hook) has too often come into operation. Additionally, in many fields the changing content and structure of knowledge growing out of research have created great need for curriculum revision. This is particularly true, of course, in the physical sciences. It is a pleasure, therefore, to contribute a foreword to the Berkeley Physics Course and Laboratory, which is a major curriculum improvement program at the undergraduate level designed to reflect the tremendous revolutions in physics of the last hundred years. The course has enlisted the efforts of many physicists working in forefront areas of research and has been fortunate to have the support of the National Science Foundation, through a grant to Educational Services Incorporated. It has been tested successfully in lower division physics classes at the University of California, Berkeley, over a period of several semesters. The course represents a marked educational advance, and I hope it will be very widely used. The University of California is happy to act as host to the inter- university group responsible for developing this new course and laboratory and pleased that a number of Berkeley students volunteered to help in testing the course. The financial support of the National Science Foundation and the cooperation of Educational Services Incorporated are much ap- preciated. Most gratifying of all, perhaps, is the lively interest in undergraduate teaching evinced by the substantial number of University of California faculty members participating in the curriculum improvement program. The scholar-teacher tradition is an old and honorable one; the work devoted to this new physics course and laboratory shows that the tradition is still honored at the University of California. Clark Kerr Foreword