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Introduction to Mechanics, Lecture notes of Physics

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An Introduction to Mechanics.

Book · February 2016

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An Exploration of The New Elementary Particle Identities from Astrophysics

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An Introduction to Mechanics

For 40 years, Kleppner and Kolenkow’s classic text has introduced stu-

dents to the principles of mechanics. Now brought up-to-date, this re-

vised and improved Second Edition is ideal for classical mechanics

courses for first- and second-year undergraduates with foundation skills

in mathematics.

The book retains all the features of the first edition, including numer-

ous worked examples, challenging problems, and extensive illustrations,

and has been restructured to improve the flow of ideas. It now features

  • New examples taken from recent developments, such as laser slowing

of atoms, exoplanets, and black holes

  • A “Hints, Clues, and Answers” section for the end-of-chapter prob-

lems to support student learning

  • A solutions manual for instructors at www.cambridge.org/kandk

daniel kleppner is Lester Wolfe Professor of Physics, Emeritus, at

Massachusetts Institute of Technology. For his contributions to teaching

he has been awarded the Oersted Medal by the American Association

of Physics Teachers and the Lilienfeld Prize of the American Physical

Society. He has also received the Wolf Prize in Physics and the National

Medal of Science.

robert kolenkow was Associate Professor of Physics at Mas-

sachusetts Institute of Technology. Renowned for his skills as a teacher,

Kolenkow was awarded the Everett Moore Baker Award for Outstanding

Teaching.

University Printing House, Cambridge CB2 8BS, United Kingdom

Cambridge University Press is a part of the University of Cambridge.

It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

www.cambridge.org Information on this title: www.cambridge.org/ 9780521198110

©c D. Kleppner and R. Kolenkow 2014

This edition is not for sale in India.

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

First edition previously published by McGraw-Hill Education 1973

First published by Cambridge University Press 2010 Reprinted 2012

Second edition published by Cambridge University Press 2014

Printed in the United States by Sheridan Inc.

A catalogue record for this publication is available from the British Library

ISBN 978-0-521-19811-0 Hardback

Additional resources for this publication at www.cambridge.org/kandk

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

CONTENTS PREFACE page xi

TO THE TEACHER xv

PREFACE An Introduction to Mechanics^ grew out of a one-semester course at the

Massachusetts Institute of Technology—Physics 8.012—intended for

students who seek to understand physics more deeply than the usual

freshman level. In the four decades since this text was written physics

has moved forward on many fronts but mechanics continues to be a

bedrock for concepts such as inertia, momentum, and energy; fluency

in the physicist’s approach to problem-solving—an underlying theme of

this book—remains priceless. The positive comments we have received

over the years from students, some of whom are now well advanced in

their careers, as well as from faculty at M.I.T. and elsewhere, reassures

us that the approach of the text is fundamentally sound. We have received

many suggestions from colleagues and we have taken this opportunity to

incorporate their ideas and to update some of the discussions.

We assume that our readers know enough elementary calculus to dif-

ferentiate and integrate simple polynomials and trigonometric functions.

We do not assume any familiarity with differential equations. Our expe-

rience is that the principal challenge for most students is not with un-

derstanding mathematical concepts but in learning how to apply them to

physical problems. This comes with practice and there is no substitute

for solving challenging problems. Consequently problem-solving takes

high priority. We have provided numerous worked examples to help pro-

vide guidance. Where possible we try to tie the examples to interesting

physical phenomena but we are unapologetic about totally pedagogical

problems. A block sliding down a plane is sometimes mocked as the

quintessentially dull physics problem but if one allows the plane to ac-

celerate, the system takes on a new complexion.

PREFACE xiii

momentum. Chapter 5 introduces the concepts of kinetic energy, po-

tential energy, and the conservation of energy, including heat and other

forms. Chapter 6 applies the preceding ideas to phenomena of general in-

terest in mechanics: small oscillations, stability, coupled oscillators and

normal modes, and collisions. In Chapter 7 the ideas are extended to ro-

tational motion. Fixed axis rotation is treated in this chapter, followed by

the more general situation of rigid body motion in Chapter 8. Chapter 9

returns to the subject of inertial systems, in particular how to understand

observations made in non-inertial systems. Chapters 10 and 11 present

two topics that are of general interest in physics: central force motion and

the damped and forced harmonic oscillator, respectively. Chapters 12–

provide an introduction to non-Newtonian physics: the special theory of

relativity.

When we created Physics 8.012 the M.I.T. semester was longer than

it is today and there is usually not enough class time to cover all the ma-

terial. Chapters 1–9 constitute the intellectual core of the course. Some

combination of Chapters 9–14 is generally presented, depending on the

instructor’s interest.

We wish to acknowledge contributions to the book made over

the years by colleagues at M.I.T. These include R. Aggarwal, G. B.

Benedek, A. Burgasser, S. Burles, D. Chakrabarty, L. Dreher, T. J.

Greytak, H. T. Imai, H. J. Kendall (deceased), W. Ketterle, S. Mochrie,

D. E. Pritchard, P. Rebusco, S. W. Stahler, J. W. Whitaker, F. A. Wilczek,

and M. Zwierlein. We particularly thank P. Dourmashkin for his help.

Daniel Kleppner

Robert J. Kolenkow

xvi TO THE TEACHER

the language of vectors and provides a background in kinematics that is

used throughout the text. Students are likely to return to Chapter 1, using

it as a resource for later chapters.

On a few occasions we have been able to illustrate concepts by ex-

amples based on relatively recent advances in physics, for instance exo-

planets, laser-slowing of atoms, the solar powered space kite, and stars

orbiting around the cosmic black hole at the center of our galaxy.

The question of student preparation for Physics 8.012 at M.I.T. comes

up regularly. We have found that the most reliable predictor of per-

formance is a quiz on elementary calculus. At the other extreme, oc-

casionally a student takes Physics 8.012 having already completed an

AP physics course. Taking a third introductory physics course might be

viewed as cruel and unusual, but to our knowledge, these students all felt

that the experience was worthwhile.

LIST OF

EXAMPLES

Chapter 1 VECTORS AND KINEMATICS

1.1 The Law of Cosines 5; 1.2 Work and the Dot Product 5; 1.3 Ex-

amples of the Vector Product in Physics 7; 1.4 Area as a Vector 8;

1.5 Vector Algebra 10; 1.6 Constructing a Vector Perpendicular to a

Given Vector 10; 1.7 Finding Velocity from Position 17; 1.8 Uniform

Circular Motion 18; 1.9 Finding Velocity from Acceleration 19; 1.

Motion in a Uniform Gravitational Field 21; 1.11 The Effect of Radio

Waves on an Ionospheric Electron 21 1.12 Circular Motion and Rotat-

ing Vectors 24; 1.13 Geometric Derivation of dˆr/dt and d θˆ/dt 30; 1.

Circular Motion in Polar Coordinates 31; 1.15 Straight Line Motion in

Polar Coordinates 32; 1.16 Velocity of a Bead on a Spoke 33; 1.

Motion on an Off-center Circle 33; 1.18 Acceleration of a Bead on a

Spoke 34; 1.19 Radial Motion without Acceleration 35

Chapter 2 NEWTON’S LAWS

2.1 Inertial and Non-inertial Systems 55; 2.2 Converting Units 63;

2.3 Astronauts’ Tug-of-War 67; 2.4 Multiple Masses: a Freight Train

69; 2.5 Examples of Constrained Motion 70; 2.6 Masses and Pulley

71; 2.7 Block and String 1 73; 2.8 Block and String 2 73; 2.9 The

Whirling Block 74; 2.10 The Conical Pendulum 75

Chapter 3 FORCES AND EQUATIONS OF MOTION

3.1 Turtle in an Elevator 87; 3.2 Block and String 89; 3.3 Dangling

Rope 90; 3.4 Block and Wedge with Friction 93; 3.5 The Spinning