Firstly, thanks to everyone above for giving some thought to these educationally fundamental, but not-directly-FSAE-related, issues. Here is some more general ranting. More specific responses next post...
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I do not blame Prof. Lewin for any of the teaching errors above. As noted, he does a great job of explaining the subject in an interesting way. The problem is with the modern education system in general, which nowadays seems to be,
"Well, it's all about this humungous jumble of equations, all of which you will have to learn. You have to learn all of them individually, because they are all a bit different. But they are also all kind of the same. Err..., in the same way that these days 'all answers are equally correct', and 'everyone's opinions must be equally respected'. Yep..., that way we can always give all the kiddies a gold-star...".
IMO the best way to teach Mechanics would be more of the Lewin/Mythbusters style of simple, real, and interesting experiments, but with much more honesty, clarity, and rigour in the explanations. This takes no more time than the current method. In fact, probably less, because most of the unnecessary equation-crunching can be dropped. So;
HONESTY - Don't tell lies about what people did or said hundreds of years ago! How is that educational?! An honest historical account is more ethical, and also often more interesting. For instance, in Newton's Definition 1 he defines the "quantity of matter" (= "mass" nowadays) as "... its density and bulk conjointly". Note how we do it the other way around these days (ie. density = mass/volume) .
Also, the notion that "We are cleverer than Newton because we know that General Relativity gives more accurate answers than Newton's ULG..." is nonsense, as noted before. High school teachers might mistakenly suggest this, but University Professors should not teach this sort of slanderous rubbish. Unfortunately, when they all do it, they can all get away with it. And all you students are the losers.
~o0o~
CLARITY - "F = P-dot" is really much easier to understand than "F = mA". I only started to think that way well after I finished my schooling, and I highly recommend it. Lewin often mentions that rotating dynamics are very "non-intuitive". This is, IMO, due to too much "F = mA". And you can forget about ever understanding gyroscopes (the most "non-intuitive" of the lot, according to Lewin) until you move to "F=P-dot". Then it all suddenly falls into place!
BTW, "Angular Momentum" (Lewin calls it L) was in the olden days called the "Moment of Momentum". It is simply the sum of all the "Moments" (= Cross-Products) of the Linear-Momentum-Vectors of the various particles and their Radius-Vectors, taken at a particular point. There is still a bit more explaining required here (maybe with some simple experiments), but seen geometrically it is all quite simple, and it gives "T = L-dot".
In the preface to Bevan's ToM book (ref'd earlier) he says "As so many of the problems which arise may be solved more quickly and easily by graphical methods, particular care has been taken to draw the diagrams correctly...". I note that in Lewin's lectures the "man climbing a ladder" problem is "solved more quickly and easily" in the simple act of drawing the FBD! (Lewin has to work through quite a lot of algebra for the same end result).
Similarly, the "time period of the hula-hoop pendulum" is solved in one, simple, do-it-in-your-head step, based on "equivalent mass systems". (Hint - What length dumb-bell has the same (2-D, planar!) mass-distribution as the hula-hoop?) And the "sliding vs rolling-ball pendulums" (ie. problem asked on other thread) is solved by simply noting the paths of motion, in side-view, of different points on the two bodies. (Hint- Which body has greater changes in its "quantity of motion"?)
Bottom line here, geometrical (or "graphical", as Bevan calls them) methods can give greatly improved insight into problems, and much quicker solutions. Your schools NOT teaching them is your loss.
~o0o~
RIGOUR - It should be constantly restressed that Newton's 3 LoMs are unprovable "Axioms", while most of the other "Laws" are deductions from these. It is a heirarchical system, starting with foundations at the bottom, and then other stuff built on top. The closer to the foundations, then the more widely applicable are the concepts. The further away from the foundations, then, typically, the more simplifying assumptions that have been used, and the LESS USEFUL is that "Law" (see eg.s below).
For a general feeling for how this works, ask the good citizens of Pisa how things go when you get the foundations wrong. Ok, so they do make some tourist-lira out of it now, but that is mainly because people enjoy looking at huge cock-ups. And the good citizens are having to pay quite a lot to prop-up their cock-up, lest it disappear into a pile of its own rubble...
As an example of the heirarchical approach, Kinetic Gas Theory is deduced from Newton's Axioms, typically with a few other assumptions thrown in (eg. the molecules are assumed to bounce off each other like elastic billiard balls). Likewise Bernoulli's Law is deduced from N's Axioms, again with a bunch of simplifying assumptions thrown in. Now, if you happen to forget any of these more superficial Laws, then, with practice, you can always re-deduce them from the very small set you started with (ie. N's I, II, & III). Fortunately, doing this reminds you of ALL those simplifying assumptions. Namely the times when said "Laws" DO NOT APPLY! (<- A hint here to FSAE-aero-guys that Bernoulli does NOT ALWAYS apply!).
An even more superficial example is the "Law of Friction", which barely qualifies for that title. Worth noting that back in the 1960s, when racing tyres started to get ridiculously wide (from 4" to 6"!, then 8"!!, then !!!) there where many experts, those that, ahem, understood the "Laws of Nature", that claimed that "wider tyres won't make any difference!". The "Friction Law" is a reasonably good approximation for hardish and smoothish materials sliding on each other, over a smallish range of pressures. But not much good for soft, sticky stuff sliding on a rough surface. And certainly no good at balancing your car's handling via LLTD and TLS.
~o0o~
Bottom line, it does not take a lot of time to constantly restress this idea that there are different "levels" of Laws (and some SHOUTING might help get the message across in less time ). The fundamentals are by far the most important, and should be understood the best. The more superficial stuff is less important, and if you happen to forget some of it, then no problem, because it is not that accurate anyway...
MOST IMPORTANTLY, never forget that the superficial stuff is usually built on a whole lot of simplifying assumptions, many of which might not apply to your particular problem!
Z