On How to Teach Engineering Mechanics

This post is almost like committing suicide. It has a targeted audience–Structural engineers within the engineering disciplines of civil, mechanical, and aeronautical engineering.

The number of people my blog posts attract, besides myself, is precisely zero. Now, claiming that the intended audience is a sub-set of a null set … that is suicide.

I am, from my current perspective, blessed to have had the opportunity of teaching the subject “Engineering Mechanics”, albeit in an extremely curtailed form vis-à-vis how and what I learned more than four decades earlier, to about 800 students over the past four and a half years. It is a compulsory course for all first year engineering students leading to a B.Tech or M.Tech degree in the institution.

This has given me the perspective that is unique (of course, the perspective of every individual on any matter is unique), in a particular sense. I have to teach students who come with different school backgrounds-CBSE, state boards, particularly of Andhra Pradesh, Telengana and Tamil Nadu-and different socio-cultural backgrounds: all levels of middle class, NRIs etc. In addition, from the perspective of “utility” of the course, one can very well imagine the range of difference in the interest students would show in the subject.

I take it upon myself to address the students in our first encounter on the complications of teaching this course, not to mention learning.

By the way, having been tuned to facing questions exclusively from the prescribed text books all through their education up until that day (with the exception of “HOT” questions in CBSE), and more importantly, with blinders on, to look at any subject within the narrow perspective of success in examinations, it is tough enough for the students as well as the teacher. Add to that, prima facie, the subject is “useless” for disciplines like computer science, information technology, biotechnology (perhaps save biophysics, a minor component, I presume), and even electrical engineering. This is a 110 m high hurdle race!

How to reduce the height of the hurdles? The following paragraphs describe a few things I do. I am not claiming any deep insight or any level of success. It is merely I do what I do, a word-to-word copy of the title of a book by the former RBI governor Raghuram Rajan. From one Raghuram to another Raghuram, it is not plagiarism, no matter what turnitin says!

All the books on the subject, most of them authored by Indian academicians (students appear to be addicted to these as these books allow them to continue “learning” the way they have done thus far), start with force systems after giving a brief on frames of reference and coordinate system.

My criticism starts here. Yes, the syllabus deals almost exclusively with fixed frame of reference. And, following the syllabus, the books mention the other types of frames of reference only cursorily, if at all. Teachers follow.

In my humble opinion (it is a different matter that I cannot have any other type of opinion) this is where the students get lost in the subject. Right here it must be mentioned-only mentioned-that all these frames of reference help us explain our everyday experiences on the earth and beyond.

A brief mention can be made that when we ride a cycle through a mild curve we can, and those amongst us who do dare will attest to the following, steer the cycle without touching the handle bar and just by inclining ourselves appropriately – an instinctive use of a non-inertial reference frame. This is why we see children, who while pretending to be flying by going around the room with their arms spread out, incline in the direction of the turning. So, I say to the students, “You see, EM merely formalizes your everyday experiences.”

I do not know whether my students understand what I say then; but, I am sure when the topic does arise later, as it does when I teach D’Alembert’s principle, I recall what I said earlier and I am sure it strikes a chord in them.

Why do we not explain spherical coordinate system using the latitude and longitude of any city anywhere in the world? We must.

I introduce Newton’s Laws of Motion and I say that almost everything we would be doing subsequently in the course is a direct consequence of those laws. Having said this, I do follow through it throughout the course. Free Body Diagram? Yes, the third law, mostly incorrectly taught and understood in high school. Friction in a body that is about to move? Equilibrium equations – the first law. Centroid, centre of mass, center of gravity – first law. Moment of inertia – second law, as applied to rotational motion. You get the drift.

I also tell the students that these concepts are used repeatedly in engineering analyses and design and stress their importance to students of civil, mechanical, aerospace streams, but do it carefully without de-stressing them for the students of other streams.

By the way, the students are astounded when I tell them that outside of our minds, there exists no entity that is called “force”. Force is just a concept. If one analyzed Newton’s second law, that is the first instance (in the European way of thinking) in which “mass” can be given an engineering interpretation – the proportionality constant connecting force and acceleration; alas, force itself is nothing physical! The basic irony of Engineering Mechanics!

We never measure a force. We know how to evaluate our concept of a force, by observing the effect this concept has on an object.

Saying all these is not a high-wire act, not at all. We are reducing the height of the hurdles gradually, step-by-step.

Towards the beginning of the semester, I emphasize the algorithmic nature of the subject. When I ask students to explain what an algorithm is, they say it is a step-wise procedure. Rote learning from their computer programming course, sad to say. Yet, not willing to look at a gift-horse in the mouth, so far so good. But, probe further, I get no responses.

Then, I refer to how a philosopher has “defined” an algorithm (I am not attesting to this definition). There are three characteristics: 1. It is a step-wise procedure and guarantees correct results (if executed appropriately and properly); 2. It is substrate independent, meaning it does not matter whether it is done by chalk on a blackboard, pen or pencil on paper, or on a super computer; and 3. It minimizes brain-work.

The last point has to be elaborated lest it be misunderstood. Devising an algorithm is a brain-intensive work, no doubt. But using it is of a very low order.

I say that the problem that is generally called the Tower of Hanoi can be solved through a two-step algorithm. But, why the algorithm works invokes inductive logic. Please, for the current instance, accept that the algorithm is truly an algorithm in the sense articulated in the three characteristics above. A more down to earth example could be how girls in the class plait their hair. It again is a two-step algorithm that requires zero brain power. I have seen girl students checking out what I say in the class discreetly with a sly grin on their face!

After grabbing the attention of the students, I go on to say that analysis of force systems should be understood as a set of algorithms, each one applicable to a particular class of problems. This is most easily done when we start with forces in three dimensions – after all we live in a three dimensional world (discount String Theory and such). And, help is on the way – vector operations, another systematic procedure, an algorithmic base. Marry the two, and, Bingo! we solve all classes of force systems. Indeed, if one dropped any one of the three axes from a three dimensional treatment of a problem, what we end up with is the two dimensional problem – the so-called “Coplanar” system.

So, despite the fact that the field has historically developed from a two dimensional to a three dimensional perspective, I consider myself as not being under any compulsion to traverse the field in the same way. I take the reverse chronological path. And, the current text book that is prescribed in the institution I work has the same directionality. Indeed, one of the touch-stones of 2-D treatment is called Lami’s Theorem. Guess what, this phrase is used, almost dismissively, only once in the above cited book without any explanations. Fancy that!

Even in tackling two dimensional problems, I have introduced certain automated manner in which forces can be resolved using minimal brain-power (read “thinking”). The same goes for problems dealing with projectile motion, another “head-ache” section. The books give examples of projectiles being launched up a slope, down a slope, from a height above the ground level, from a depth below the ground level and every other way imaginable. I give students only one equation and boldly claim-and surprisingly, in the most recent internal evaluation test, a student of mine did use only that equation!-that this is the only equation they need, keeping in mind all the other procedures of aligning the input data to the requirements of the equation.

In fact, I treat projectile motion as a special case of orbital motion (treated in the simplest way-no equations-and in not more than one lecture) and justify one of the two assumptions we make.

I now come to the aspect of assumptions. In the first class itself I insist that my students ask, and hopefully get clarified, why we make this or that assumption. Students do not necessarily do what I ask them to do–universal experience, I believe-and, I Suo Motu give the explanation for each of the assumption; by the way, this is a habit of mine even in the higher classes. This is necessary because we have to tell the students that EM is nothing but high-flying pure mathematics brought down to earth to tackle everyday problems.

This is my way of responding to my earlier question, “How to reduce the height of the hurdles?” I do not know whether I have indeed reduced the height of the hurdles, but none can gainsay that I have tried.

I know this has been a long rant. I would stop now. As I have said earlier this is what I do. If the reader finds positive teaching take-aways in it, she is most welcome to adopt. Indeed, I would request him to teach me how to go at least one better than what I am doing now.

As I often say to myself, I am a full-time learner and a part-time teacher.

Raghuram