Learning and teaching Mechanics at the undergraduate level – Debut of an exciting new textbook

Preface

Ernest (Lord) Rutherford, one of the greatest physicists of the last century and the father of Nuclear Physics, may have put his foot in his mouth when he said; “Physics is the only real science; all else is stamp collecting”.  However greatly such  a wild statement may offend non-physicists, the fact remains that physics is really the mother science around which other sciences have grown, ‘generating the fundamental knowledge needed for technological advances that will continue to drive the economic engines of the world’.

If Physics is at the heart of the sciences, Mechanics, which is essentially a study of different types of motion of all kinds of material objects in the universe and the forces acting on them, is really at the heart of Physics.  Whether it is the motion of electrons inside atoms or of atoms and molecules inside matter in any of its states or of the motion of different parts of any machine or of the planets around a star or of the growth of plants or animals on earth, motion of an object with reference to an appropriate frame of reference is perhaps the single most important property that needs to be studied in great depth.  This is the domain of Mechanics, both the classical and quantum varieties.  A real understanding of physics is not possible without a deep understanding of Classical Mechanics where Newton’s laws of motion and their manifold applications play a crucial role.

 

A deep understanding of Mechanics is therefore essential in any physics education programme at any level, particularly at the undergraduate level where it is a pre-requisite for understanding other disciplines.  Unfortunately, this is not being achieved adequately for a variety of reasons, especially for want of a rigorous mathematical approach to learning Mechanics that is so essential for the application of both in problem solving situations.

The needs of junior college education in physics are met by a variety of good curricular materials and outstanding textbooks such as Fundamentals of Physics by Resnick, Halliday and Walker.  The situation is not so good when it comes to undergraduate and graduate levels, primarily because of lack of textbooks combining a rigorous mathematical approach as stated earlier with a style and substance that captures the learner’s interest and attention, yet not employing discouragingly advanced mathematics.  It is in this context that I find great pleasure in introducing and reviewing a new textbook that has just been published in India and elsewhere by Pearson Education publishers.  The author of this book, simply titled ‘Mechanics’ (it could as well have been titled ‘Classical Mechanics’), is a former professional colleague and a great friend of mine, Professor Somnath Datta.

The Publication

Here is a picture of the obverse and reverse title pages of Dr Somnath Datta’s book that is now available in the market:

Containing 14 chapters, two appendices and running to 630 pages, this paper- back publication was composed entirely by the author himself with the LATEX software package, thus making the task of the publishers quite easy.  A uniquely distinctive feature of the publication is the presence of a large number of excellent figures/drawings/illustrations all of them meticulously designed and generated again by the author, and many of them to realistic scale, using the Gnuplot package in conjunction with LATEX and the Linux OS.  He has explained in some detail how he did this in the second of the two appendices.  While these are of superb quality, many of them deserve to be printed in a larger size and on better quality paper to do justice to the effort put in.

 

The following is a somewhat randomly chosen example of the richness and quality of the illustrations, featuring the scattering of alpha particles by a gold nucleus plotted precisely to scale.  Incidentally, it is one of the numerous worked-examples in the text and rather coincidentally focuses on the historic work of Lord Rutherford whom I have quoted at the very beginning of this post.

The monumental preparatory work put in by the author, coupled with minor compromises in the quality of production, has made it possible for the publishers to offer the book for sale at an unbelievably affordable price.  One can have it delivered at home for an all-inclusive cost of just Rs. 290 (inclusive of an introductory discount of Rs. 35) anywhere in India by placing an order online at:  http://pearson.vrvbookshop.com/book/mechanics-somnath-datta/9788131773734  I have ordered one to be gifted away to a serious student, having already gone through a complimentary copy given to me by the author very thoughtfully.

  

The Motivation

In his own words, Dr Datta’s prime motivation for writing this book is summed up by the following statement appearing in its Preface:

My long-standing involvement with teacher-education has shown me the wide gap between the expected standard (of learning) and reality.  I have been concerned about the state of physics education, especially the level of understanding of students and teachers at the secondary and higher secondary levels.  Misconceptions are widespread.  Elementary principles are scarcely understood.  Terms like centripetal and centrifugal forces have played havoc.  Newton’s third law of motion is totally misunderstood and thoroughly misinterpreted.  Even some textbooks have the same mistakes.

The author and I have often shared with each other our serious concern for the quality of learning with regard to the basic concepts of  mechanics and hence of the whole of physics.  I have some empirical data to highlight this in respect of both teachers and students and intend to feature them in a future blog post of mine.  In essence, there seems to be little difference between the contemporary understandings of the concepts and those that existed intuitively during the Aristotelian past, even among many who profess an education in physics.

  

The Contents

Since vector algebra and calculus are liberally used throughout the textbook, the initial chapters are understandably devoted to an exposition of these topics as preparatory to an understanding of mechanics and the rest of physics as well.  Conservation of linear momentum is dealt with in chapter 4, followed immediately by Newton’s Second Law of Motion and its applications.  Chapter 6 deals with the Law of Gravitation (more on this later) followed by Newton’s Third Law of Motion which the author so rightly describes as ‘totally misunderstood and thoroughly misinterpreted’.  Here he breaks away completely from the normal style of  presentation and develops the concepts though hand-written drawings forming a slide show that he had developed earlier specifically for the purpose.  In the same chapter he focuses strongly on the use of free body diagrams and their problem solving capabilities.

 

The concepts of work and energy are dealt with in chapters 8 and 10 interspersed with chapter 9 dealing with motion under central forces, drawing heavily upon examples from Astronomy and Space applications.  After describing the properties of fluids, both at rest and in motion in chapter 11, the focus shifts to systems of particles and rigid body dynamics in the next chapter.  As a prelude to the last chapter on relativistic mechanics, chapter 13 deals with forces and motion in non-inertial frames of reference.

The textbook is embellished with 180 illustrative examples worked out in considerable detail and about as many end-of-chapter exercises to be attempted by the student.

 

Unlike many other books of its kind, this one does not discuss the very elegant Lagrangean formulation of mechanics.  The author justifies this by saying that his principal concern has been to put Newtonian Mechanics on a sound footing and considers such foundation to be of overriding importance.

Newton and Gravitation

 

For me, chapter 6 dealing with the Universal Law of Gravitation is the centerpiece of the whole textbook because of its wonderful blend of history with the physics of the phenomenon that literally binds everything in the universe, and the universe itself, together.  The author sets the stage for it with the following profoundly simple introductory remarks:

Few greater tributes have been paid to the genius of Newton who drew upon the work of his predecessors – Copernicus, Tycho Brahe, Johannes Kepler and the great Galileo himself – and developed the laws of (classical) mechanics that form one of the greatest and most enduring edifices of science.

The author goes on to make an extensive and masterly quantitative and graphical analysis of the paths of planets Venus and Mars from both the geocentric and heliocentric viewpoints, draws relevant conclusions and shows how they eventually led to Kepler’s laws of planetary motion and subsequently, and even more importantly, to Newton’s law of Gravitation.  The following full page picture represents the analysis of the path of planet Mars that was to lead Kepler conclusively to his second law of planetary motion (the figures look better when enlarged and in the printed version of the book).

  

For an article titled, “A Brief History of Gravitation: Copernicus to Newton” published in the online version of Physics Education, the reader may refer to:

http://www.physedu.in/uploads/publication/2/50/28.2-4PESomnathDatta.pdf

Other Features

Unlike conventional textbooks on Classical Mechanics, this book draws its examples liberally from other areas of physics such as electrodynamics, atomic and nuclear physics, etc., apart from a distinct bias for astronomy and space science related examples.  This way it promotes a holistic view of physics as a discipline without artificial barriers.  It also brings out the absolutely indispensable role of mathematical methods in solving problems in the world of physics.  The consistent and systematic use of vector methods, often unappreciated by students and teachers, is especially noteworthy.

The following is a figure that may appear to have been taken straight out of a textbook on Electricity & Magnetism, but actually appears under Newton’s Second Law of Motion in chapter 5 of this book on Mechanics.  The motion of a charged particle in an electric field discussed here and illustrated in such meticulous detail certainly merits a place in the book which implicitly doesn’t recognize artificial boundaries or barriers among different areas of physics.  Incidentally, the principle finds an application in conventional TV sets.

The book is not geared to any specific syllabus of any Indian or foreign university system, with its content determined by the author’s perception, based on long experience, of what should go into a useful course on Mechanics in relation to Physics as a whole.  Yet it meets the needs of most university systems and should be welcomed by any serious student of Physics.

The Author

Starting with a degree in Civil Engineering in which he obtained considerable proficiency as exemplified by his technical drawing skills demonstrated in this book and elsewhere, Dr Datta developed a love for physics and obtained his doctorate degree from the University of Illinois at Urbana-Champaign.  After returning to India, he joined the Regional Institute of Education (NCERT) at Mysore as a colleague of mine.  He chose to retire voluntarily from his NCERT service and concentrate on teaching of physics at the University of Mysore as a guest faculty in its post-graduate department of Physics.  He has also been involved in the design and fabrication of a variety of teaching aids and the production of video programmes for physics education.  His main focus continues to be on his writing efforts and on honing his considerable artistic talents.

 

Apart from his numerous contributions in physics and physics education through publications in reputed international and national journals, Dr Somnath Datta is also the author of a book titled “Introduction to Special theory of Relativity” first published in 1998 by Allied Publishers.  He is currently hard at work on another of his major writing projects, a textbook on Electrodynamics.  His numerous friends and I are eagerly looking forward to its early completion and publication.

Dr Datta is as devoted to music and performing arts, especially Rabindra Sangeeth and the great dance dramas of Rabindranath Tagore, as he is to Physics and spends most of his time on both.  One of my earlier blog posts [See: 11) Tagore and Einstein on Music (Aug 10)] makes a pointed reference to his musical talents.

The Triumph

The achievement of writing a book of this high caliber is impressive enough from any person in any situation.  It is much more so when one realizes that Dr Datta has done this against extraordinary odds, fighting a long battle against prostate cancer with which he was diagnosed even before he started writing this book.  It is a tribute to his extraordinary and incredible spirit, courage, and persistence that he has not only carried out his task successfully but also won the battle against such a deadly enemy.  When he visited me last week at my home to give me the complimentary copy of his book, he appeared as cheerful and normal as anyone can be.  Had I not known about what he had been going though I would never have suspected that anything was wrong with him.  To me his achievement is as heroic at the intellectual plane as that of the Marathon Man of Mysore that I recently wrote about [See my blog post: 54) Marathon Man from Mysore and his magnificent obsession – Three monumental feats of endurance and courage (Aug 12)].  I am now pretty sure that it is only a matter of time before his book on Electrodynamics comes out and I will have the pleasure of reviewing it as well.