From the Book Shelf . . .

An Introduction to Mechanics

by Daniel Kleppner and Robert J. Kolenkow

McGraw-Hill International Edition,

Singapore, 1978

ISBN 0-07-085423-8

Price: Rs. 500

The book under review is used as a text material for PHY101 which is one of the core UG courses offered in the first semester. The course contains some topics that the students are supposedly familiar with, which include Newton's laws of motion and their applications, friction, conservation principles, etc., and some new topics such as the use of polar coordinates, variable mass system, central forces, rigid body dynamics in two and three dimensions, motion in noninertial frames, damped and forced oscillations, special theory of relativity, etc. Although no single book meets the requirements of the course entirely, the book under review has been found to be useful .

The authors have addressed themselves to the reader's analytical skills as well as the ability to select appropriate tools for problem solving. Considerable effort has gone into maintaining a balance between the mathematical rigour and physical picturization of a situation. A number of illustrative problems solved immediately after introducing a new concept contribute to the assimilation of the ideas. The problems given at the end of each chapter are well designed and graded according to the difficulty level.

With all the ingredients of a very good textbook, the book under review remains, in my opinion, an instructor's book and not the student's book. Quite often the mathematical details are not all that necessary and students would be tempted to skip these portions to go ahead. But in these apparently less needed portions, sometimes important issues are raised. An instructor can organize the relevant issues in his lecture plan to make a more effective use of the book. Some chapters carry additional "notes" at the end which are intended for the students with a relatively advanced mathematical background.

Chapters 1-4 deal with vectors, kinematics, Newton's laws of motion, linear momentum and energy. Although the students are familiar with these topics from school, they are bound to come across a new vision here. Sections 1.9, 2.5, 3.5, 4.9, 4.10 and 4.14 may be studied

thoroughly as these present crucial new concepts such as plane polar coordinates, everyday forces in Physics, variable mass system, energy diagrams, small oscillations and collisions in the centre-of-mass frame.

Chapter 5 deals with relations between force and potential energy. Although these topics are quite useful in offering an understanding of the nature of conservative and nonconservative forces, the description is mathematically more sophisticated than in other chapters. However, since many of the mathematical tools used here, e.g., gradient and curl of fields, Stokes theorem, etc., are covered in detail in the concurrent Mathematics course, the description should not be very cumbersome to follow.

Chapters 6 and 7 discuss angular momentum and rigid body motion. Most of the students need thorough practice in these topics and the large number of worked out examples provide a very useful material for this purpose.The detailed treatment of gyroscopic motion given in Chapter 7 could be considerably reduced.

The use of rotating frame of reference is given in Chapter 8. The subject is developed in a simple fashion and very good examples are used to illustrate the techniques. The central force motion in two dimensions is developed in Chapter 9. Most of the discussion is based on energy diagrams, which provide a clear understanding of the motion. Planetary motion is discussed using the differential equations of orbit with good supporting examples. Damped and forced harmonic oscillations are described in a somewhat traditional manner in Chapter 10.

Chapters 11-14 deal with special theory of relativity. Only a small portion of this extremely interesting and important area is generally covered in PHY101.

To summarize, An Introduction to Mechanics by Klepper and Kolenkov is a useful book for PHY101. However there are portions which may be condensed or skipped altogether, either because of their elementary nature or because they are pitched at an advanced level. Even in these portions, there are important tips for the instructor which should not be overlooked.

H.C. Verma

Department of Physics

IIT Kanpur

e.mail: hcverma@iitk.ac.in

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