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From: YoungGandalf DelphiPlus Member IconJan-8 1:53 PM 
To: All  (1 of 6) 

This coming spring term I will have to teach two new classes and I will use this diary to jot down some reflections I’ll have about the material and the about how the students cope with the course. Classical Mechanics is our first theoretical physics course. In the series of theory classes, we take the material that has been introduced in an experimental class before, and take it to a new, more contemporary level. Mechanics is often the first of such. Other similar courses include E&M (usually as E&M1 and 2), Quantum Mechanics (to extend modern, atomic, and nuclear physics), and Stat Mech (to extend thermal physics).

As usual, I will change names even though it is a long shot for anyone to figure out who I am actually talking about. My long-term colleague David retired with short notice at the end of December. Our department was very strained to offer all courses for spring. I was the only realistic option for two classes to take over, and this is one of them. I have never taught it before, so this is a bit of an adventure.

Students are planning to take this as their first serious major class in their second sophomore term. The weakest students will normally not make it here. These thirteen students made it here:

Mel, a grad student in Math; Max, a Mechanical Engineer with a minor in physics (this is usually one of four classes minors have to take beyond the two introductory physics courses 1 and 2), he took a Physics 1 class from me two years ago and defined the top of the class then; Trevor, a double major from Physics Education, apparently, I had him once before - I do not remember him; Caleb, an Astronomy major I have not met in class yet; Eidan, a transfer Physics major who has now completely switched to us (I had him last term in Stat Mech - as a transfer, Eidan takes courses out of order); Reese, a physics major I have not met yet; Gabby, an astronomy major I had in Physics 1 and over summer in Physics 2; Willem, a new transfer astronomy major, his transfer record looks a bit troubled; Corinne, a physics major I had during covid indirectly when I had to take over a colleague’s online class last year; Chris, a Math/Physics double major who I recruited two summers ago when he took my Physics 1; Mason, a Physics Education double major who I had in Physics 2 last term, he is an athlete in the football team and carries an incomplete in Physics 2 with him; Britney, another Physics Education double major, I do not know her yet; Jaclyn, a physics major with a troubling record (failed Physics 1 the first time, took it over summer with me and got a D and took last term my Physics 2, which she finished also with a D).

Lecture one will largely be consumed by talking about the syllabus. The remaining lecture will be used to lay out to the students what the course is about, how it relates to their prior course on Newtonian Mechanics, and how it differs.

I will start that section with an interactive part in which I make the students remember what they have learned and what they have not learned. In that initial assignment I hope students to come up with two memories: Newton's Laws plus the Law of Gravitation, sometimes known as Newton's Fourth Law, and Conservation Laws (for Energy, Momentum and Angular Momentum). I will also make them confront what they did not learn: what the exact nature of the premises of Mechanics are: space, time, and mass. These students will be taking Modern Physics in parallel, a class where I do a similar warmup when I teach it. But this term a Taiwanese colleague is teaching that class and he will likely do a much drier, not conceptual introduction. So I won't rely on what they may or may not learn there and do the parts I need for this course myself.

From there I will go into an overview lecture that starts with what the students are familiar with, but put it into a new light and context, and then augment it with an outlook how we will be changing it. It goes something like this:

(Remember, the students have just recalled the Conservation Laws)

The principle of Conservation of Momentum is a consequence of Newton's Third Law. (in our abbreviated treatment in physics 1 this will not have been on the menu)

Consider a vertical rocket launch. You may think "Apply Newton's Second Law and solve". But that does not work because the mass of the rocket is changing continually as the rocket is being pushed by a force. Newton was aware of this difficulty and saw that it is corrected by equating the force to the rate of change of its momentum. With this in mind, one can calculate the force acting on the rocket in two steps. First, treat the rocket at any moment as though its mass was constant and multiply the mass by its acceleration at that moment. Then treat the velocity as not changing and multiply it by the rate of change of mass at that moment.

The force acting at that instant is the sum of these two products: m dv/dt + v dm/dt, where the terms dv/dt and dm/dt refer to the calculus, that is the derivative of velocity v and mass m with time t. Stated this way, the Second Law indicates that momentum is a candidate for conservation.

Momentum Conservation implies a spatial symmetry of laws of nature because the calculation is the same, regardless where one measures from (where we assign the origin).

Just so, Energy Conservation means a time symmetry of laws of nature (remember that in the StatMech class I drew on that when I introduced entropy), because it is invariant with respect to a shift in time.

This means that if some physics process is some function of space and time (as my students know they always are), then momentum p is related to how the state changes from point to point in space. And energy is related to how the state changes from moment to moment in time. This intrinsic coupling, if you will, plays a very important role in Quantum Mechanics, for example in the Heisenberg Uncertainty Relation, which states "change in momentum times change in position is bounded by a minimum value", the Planck quantum. And similarly, :change in energy times change in time is bounded by the same quantity.

Most of the time we do not think of Newton's Laws as applying to rotational motion, but they do. Moreover, pure translational motion rarely occurs in nature. To better understand the implications, let's first think about pure rotational motion (like a wheel turning on a stand but not moving anywhere). In pure rotation, no straight line remains parallel to itself, except the axis of rotation. Newton's Laws cannot be applied directly, one has to enlarge the formalism:

A force acts on a particle to keep it moving in a circle. Its momentum is not conserved. But its angular momentum is: a new vector of magnitude mvr that points along the axis of revolution. It is related to a variation of force, the torque tau. In linear mechanics we had dp/dt = F, that is the rate of change of momentum p in time t is the Newtonian force F. Here we find that the rate of change of angular momentum L in time is torque: tau = dL/d
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  • Edited January 10, 2022 12:26 am  by  YoungGandalf
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From: YoungGandalf DelphiPlus Member IconJan-19 10:19 PM 
To: All  (2 of 6) 
 14742.2 in reply to 14742.1 

One insight from all three courses on the first day of class was that they all started out slow. Slower than my plan. I will have to see if I can speed this up or whether the covid demon can manipulate us.


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From: YoungGandalf DelphiPlus Member IconMar-24 11:23 AM 
To: All  (3 of 6) 
 14742.3 in reply to 14742.2 

The Classical Mechanics class has been a mixed bag so far. There is a core group that sticks together. Some of them are struggling, some excel. Hopefully, they will help each other out.

Then there are some peripheral students, Max, who is not as strong as I remembered him to be. Trevor, who struggles getting homework in on time and whose grade suffers from some lower scores because he turned in only a half homework now and then. Britney, who is a worker bee and has been doing well. Chris is a serious student, too, but he struggles with the material. There are also the no-show students like Jose, who is also a no-show in Math Phys. Mel did withdraw from class before term. Mason, the athlete, is also a no-show, but he hands all assignments in and did okay on the midterm, in the C range.

The core group, Jackie, Gabby, Corinne, Eidan, Willem, Reese, and Caleb is largely also in Differential Equations, the class that is taught right before my class and which is highly relevant for what we do. Eidan is sweet on Corinne, which changes the class dynamics at times quite a bit.

Anyhow, the Math class is a disappointment to students, I can tell from their conversations when I come to class. The teacher is Chinese. Their midterm there was one week before mine and was to be handed back the day before spring break. The teacher said to them that he won’t hand the exam back yet but that the exam was so bad that he wanted them to decide right now whether they wanted a doover exam. The new score would count. What an awkward outcome! What if a student did well enough on the first exam but does not know it?

Anyhow, the two classes teach some parallel subjects almost at the same time, and I can tell that it would be useless for me to rely on the math class teaching the math aspects efficiently. So I teach them myself, which is a major inconvenience and it makes the physics side come short.

I had a good sense for what was coming and adapted my exam to test what the students knew, not how much they did not know. I gave them six problems, they had to do three. In that way, a student is not forced to deal with a topic they do not understand. As long as there is any topic they do understand they can come out with a reasonable result. I use that as a confidence builder and as a life line.

I also added a problem that was open. It stated: It is possible that you have worked very hard and prepared for problems I did not happen to test. Define such a problem here and show your solution for it.

That is in the spirit of testing what they know. Some students make good use of it and some did not do that problem at all. In the end, the trick of just three problems worked well enough. Most students got at least a C grade, most a B or an A, and a few students got worse than a C still. However, the students knew at the same time how much they had not retained, and I am trying to use the exam life line to convey this message: you can pass this class, but you have to work hard as the new material builds on the old and will be more difficult. Come for help if and where you need it.

I started to offer a voluntary discussion where we do problems. Attendance is good. I am hopeful that this class will help borderline students to turn it around. At the same time, it does little for the too weak students. Willem, Corinne, Jackie, and Trevor are borderline. Mason is hard to evaluate. Reese and Eidan build the top of the class, Gabby is a close runner-up. Max, Caleb, Chris and Britney will be okay, probably low Bs.

  • Edited March 24, 2022 11:48 am  by  YoungGandalf

From: VERNADEEMar-28 11:32 PM 
To: YoungGandalf DelphiPlus Member Icon  (4 of 6) 
 14742.4 in reply to 14742.3 


Re<<Chinese math teacher>>

My husband once took college calculus from a Chinese teacher, which went fine until _after the drop date_ when there were only a couple Caucasians left in the class and started teaching in Chinese.  My husband asked why and was told that since the majority of students were Chinese speaking it made sense to teach the class in a language that they were most familiar with.   He ended failing the class and had to retake it from someone else.  His dean would not believe the associate professor would do that and threatened to toss my husband out of school when he offered to record a lecture.  But eventually he did pass Calculus with a high B.  He is German and very very stubborn.  <G>



From: Ishmael112Apr-2 8:06 PM 
To: VERNADEE  (5 of 6) 
 14742.5 in reply to 14742.4 

Your husband's experience of having to attend and fail a course taught in Chinese is an example of the kind of power professors have over students.  Fortunately, most do not do that kind of thing.  But when it happens it can be a real disaster.  


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From: YoungGandalf DelphiPlus Member IconApr-2 8:16 PM 
To: Ishmael112  (6 of 6) 
 14742.6 in reply to 14742.5 

In most classes, if that happened today, the university would be threatened to get sued and there would be a quick remedy.


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