Physics 351 — Friday, January 16, 2015

I You read Chapters 2+3 for today.

I 35/40 of you answered the reading questions this time. A fewhave already done next week’s reading.

I Many of you are pointing out to me nice examples of howTaylor’s review of freshman physics is filling in gaps that you’dmissed, or whose derivation you’d forgotten.

I Skim Chapter 4 for Wednesday (1/21).

I Homework #1 due next Friday (1/23).

I Today: finish course overview + Chapter 1. I also found agood excuse for a short Mathematica introduction.

I Let’s start with syllabus, schedule, course policies, etc., sothat we can vote on times for Wed + Thu “study sessions.”

positron.hep.upenn.edu/p351

From Richard Feynman (Feynman Lectures):I “I think, however that there isn’t any solution to this problem of

education other than to realize that the best teaching can be doneonly when there is a direct individual relationship between a studentand a good teacher — a situation in which the student discussesthe ideas, thinks about the things, and talks about the things. It’simpossible to learn very much by simply sitting in a lecture . . . .”

From Mary Boas (Mathematical Methods):

I “One point about your study of this material cannot be emphasizedtoo strongly: To use mathematics effectively in applications, youneed not just knowledge but skill. Skill can be obtained onlythrough practice. You can obtain a certain superficial knowledge ofmathematics by listening to lectures, but you cannot obtain skill thisway. How many students have I heard say, ‘It looks so easy whenyou do it,’ or ‘I understand it but I can’t do the problems!’ Suchstatements show lack of practice . . . .”

To whatever degree is feasible, I’ll try to focus the time you spendfor this course on solving (worthwhile) problems. I’ll also try tofacilitate your “talking about the things” with me, Tanner, andeach other as much as possible.

Two representative responses to my “what did you finddifficult/interesting” question for Wednesday (Chapter 1):

I “Since I took 150 (not 170), Newton’s laws in polarcoordinates are new to me, but they were not difficult tounderstand. I didn’t expect to encounter anything I didn’tknow in Chapter 1.”

I “I found the derivation of the polar coordinate form ofNewton’s second law very interesting, even though most of it Iknew from phys 150. The textbook was very clear and I amlooking forward to reading more from this book.”

So let’s go through Newton’s second law in 2D polar coordinates.(On the board, but I copied my notes into these slides.)

Constant r case (familiar): a = r̈ = −ω2rr̂ + αrφ̂Constant φ case (line through origin): a = r̈ = r̈r̂Notice if Fr = 0 and φ̇ = constant (say φ̇ ≡ ω) then

r̈ = ω2r ⇒ r ∝ cos(ωt− δ)

The two particularly interesting terms in the 2D polar form ofNewton’s 2nd law are called the “centripetal” acceleration and the“Coriolis” acceleration. We’ll study the Coriolis effect formally inChapter 9.

But now that we’ve mentioned the pseudo-forces that appear innon-inertial reference frames, let’s spend 3 minutes on a fundemonstration of the Coriolis effect, which also serves as an excuseto show you how you can take your first few steps in Mathematica.

(This vaguely relates to Problem 5 on HW #1.)

It turns out to be surprisingly easy to use Mathematica to graph(and even animate) what we see in this demonstration. See“notebook” at

positron.hep.upenn.edu/p351/files/0116_coriolis_pendulum.nb

Physics 351 — Friday, January 16, 2015

I Skim Chapter 4 for next Wednesday (1/21). Slow down forany parts that feel less familiar (e.g. 4.5, 4.7, 4.8).

I Remember online questions for each reading assignment.

I Homework #1 due next Friday (1/23). (Printed handout, alsoavailable online.)

I Did I remember to poll the class about Wednesday &Thursday study-session times?

I Some people cite angular-momentum derivations as trickestpart of Chapter 3. Shall we go through that on Wednesday?

I Email me if you need a Mathematica license. I highlyrecommend the “Hands-on start to Mathematica” 80-minutescreencast, which takes about 2.5 hours to go through(pausing as you do what the presenter does).

http://www.wolfram.com/broadcast/screencasts/handsonstart/