What keeps electrons spinning around their nucleus?
in [Relativity]
|
From: Gregory L. Hansen on 30 Mar 2005 10:24 In article <kvhk41ldc9goslnkrie17olvlohgqe7d3v(a)4ax.com>, David Cross <spamdenied(a)nospam.net> wrote: >On Wed, 30 Mar 2005 03:45:34 GMT, "Bill Hobba" <bhobba(a)rubbish.net.au> wrote: >> >>Having studied physics after completing a math degree I had the same >>experience. Trouble is I ran into the problem Feynman alluded to - the math >>can hide the physics. > >What had happened for me was that we were learning about the forces exerted by >magnetic fields, and the professor, although he didn't have to, taught the >cross-product form of the F = qvB sin theta equation in order to get us to >understand the physical significance of the perpendicularity of the force to >the velocity and field vectors. > >As a result, when I came across r x F (that is, rF sin theta), I didn't have >to be sidetracked by rather strained explanations for explaining why the units >of torque are Newton-meters and why the torque was perpendicular to the force >and the radial direction. I just had to skip past all that and realize that >the physical significance is the same as that for the qv x B :) The physical significance of the torque pointing perpendicular to the force and the radial direction had me completely mystified as a freshman. And much later I learned that in the wedge product they don't even bother; if the lever arm is pointing in the direction e_x and the force in the direction e_y, the torque is in the direction e_x^e_y. In three dimensions, and only in three dimensions, you can find a unique axis of rotation that defines a plane of rotation. In more dimensions, all you can do is give two vectors that define a plane of rotation. I think my freshman prof might have done more to emphasize that the direction of the cross-product is a convention. -- Irony: "Small businesses want relief from the flood of spam clogging their in-boxes, but they fear a proposed national 'Do Not Spam' registry will make it impossible to use e-mail as a marketing tool." http://www.bizjournals.com/houston/stories/2003/11/10/newscolumn6.html
From: David Cross on 30 Mar 2005 10:43 "PD" <pdraper(a)yahoo.com> wrote in message news:1112193095.258819.36760(a)l41g2000cwc.googlegroups.com... > the wheel with a modified shoe polisher, and we would all point in the > direction of the wheel's angular momentum, and then point to the board > where T = dL/dt was written, and *predict* what would be different in > this case before I let go. When I finally released the other end of the > axle and let it precess, I could look out into the classroom and see > palpable mental victory and sudden, profound appreciation for the cross > product. They could *see* the vectors extending from the wheel as it > hung there. (We would then slow the wheel to change the rate of > precession, or change the spin direction of the wheel, just to pound in > the point, but by that time, they were way ahead of me.) That's right; I remember the bicycle wheel demonstration in my physics lectures as well, and seeing it precess around its axis was pretty damn-all neat. I also just quickly worked out the vector changes and it's still just as neat as the day I saw it :) -- David Cross dcross1 AT shaw DOT ca
From: mmeron on 30 Mar 2005 15:25 In article <osu2e.17659$C7.3333(a)news-server.bigpond.net.au>, "Bill Hobba" <bhobba(a)rubbish.net.au> writes: > ><mmeron(a)cars3.uchicago.edu> wrote in message >news:Zcr2e.42$45.5559(a)news.uchicago.edu... >> In article <lrm2e.17108$C7.9311(a)news-server.bigpond.net.au>, "Bill Hobba" ><bhobba(a)rubbish.net.au> writes: >> >> Seeing how Landau wasn't above >> >> mentioning both centrifugal and coriolis forces in his Mechanics, is >> >> see no reason for purism here. >> > >> >He sure did. But notice he makes it clear they are the result of using >non >> >inertial frames to write the lagrangian in. >> > >> Did I (or anybody else here) said otherwise? > >Sorry Mati - it is obvious I did not express what I wanted to say well >enough. I was not questioning anyone thinking or saying differently - I was >simply passing a comment. > Ahh, OK. Of course, I fully agree. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: mmeron on 30 Mar 2005 15:38 In article <e9adncBCPNmLCdffRVn-uw(a)rcn.net>, jmfbahciv(a)aol.com writes: >In article <f1l2e.34$45.5068(a)news.uchicago.edu>, > mmeron(a)cars3.uchicago.edu wrote: >>In article <pPmdnT872IUW8tTfRVn-rw(a)rcn.net>, jmfbahciv(a)aol.com writes: >>>In article <7K52e.21$45.3808(a)news.uchicago.edu>, >>> mmeron(a)cars3.uchicago.edu wrote: >>>>In article <Xns9627C5AEB62D6WQAHBGMXSZHVspammote(a)130.39.198.139>, bz >>><bz+sp(a)ch100-5.chem.lsu.edu> writes: >>>>>mmeron(a)cars3.uchicago.edu wrote in >>>>>news:8B12e.18$45.3391(a)news.uchicago.edu: >>>>> >>>>>> In article <Mo12e.16031$C7.902(a)news-server.bigpond.net.au>, "Bill >>>Hobba" >>>>>> <bhobba(a)rubbish.net.au> writes: >>>>>>> >>>>>>><mmeron(a)cars3.uchicago.edu> wrote in message >>>>>>>news:XQ02e.15$45.3352(a)news.uchicago.edu... >>>>>>>> >coordinates, but I think what is misleading is to call the >>>correction >>>>>>>> >terms "forces". >>>>>>>> >>>>>>>> Only if you attach more meaning to the term "force" than it >deserves. >>>>>>> >>>>>>>Ahhhhhh. Yes. As Feynman says it is half a law. It gains its full >>>>>>>meaning when combined with other laws and/or concepts such as >Coulombs >>>>>>>law or the introduction of non inertial reference frames. >>>>>>> >>>>>> Yes, it is a rather complex issue. I wrote some stuff about it in >the >>>>>> past, here, but I never kept a copy. But it certtainly needs some >>>>>> sort of broad framework, to make sense. >>>>> >>>>>Especially when someone keeps insisting that force is always the result >>>of >>>>>acceleration >>>> >>>>Cause, not result. >>>> >>>>> and that without acceleration (as for example when a gyro >>>>>precesses at a constant rate, or when a mass moves at a constant >velocity >>>>>because it is overcoming drag or friction) there is no force and no >work. >>>>> >>>>Where there is net force, there is acceleration. The F in Newton's >>>>law is the total (i.e.) net force acting. Since forces are vectors, >>>>it is perfectly possible to have different non-zero forces to sum up >>>>to a zero net force. >>> >>>This is why using algebra in first physics courses hurts learning >>>more than it helps. >>> >>I don't see why it should hurt. Of course, it is better if you can >>use calculus, not just algebra. > >Oh, it hurts because the concept of changes doesn't show up >when doing the math. Well, that's true. Newton had good reasons to create calculus, without it you're mostly limited to static situations. Unfortunately, though, high schools teach calculus late (if at all). Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: mmeron on 30 Mar 2005 15:42
In article <RtidnWcXTP7uC9ffRVn-2Q(a)rcn.net>, jmfbahciv(a)aol.com writes: >In article <07n2e.41$45.5359(a)news.uchicago.edu>, > mmeron(a)cars3.uchicago.edu wrote: >>In article <GJk2e.16991$C7.9156(a)news-server.bigpond.net.au>, "Bill Hobba" ><bhobba(a)rubbish.net.au> writes: ><snip> > >>>> That said, there is certainly room to analyze the way things are being >>>> taught. The natural tendency is to teach things in the historic order >>>> in which they were developed (an educational equivalent of "ontogeny >>>> recapitulates philogeny"). That may not necessarily be the best >>>> course of action. >>> >>>Having read the replies by yourself, Gregory and PD I relise in >suggesting >>>that I had forgetten one of the things I emphasize in education. It must >>>actually be tested rather than be based on what I or others may think >>>belongs in a course. >>> >>Aye, exactly. > >The Mass. board of education is now trying to add science >as part of the high school graduation requirement. The >year proposed was 2008 but news broadcasts are now saying >it can't happen until 2010. Listen for the whinging from >teachers' unions. One of them is already running ads that >they can't teach science because there is only 1 microscope/ >10 students. Since not all students (not even a majority of students) take classes requiring a microscope at the same time, I don't see a problem here. > That's an awfully high ratio even though the >ads want you to think that it's too low. When I went to >high school, I estimate the ration to be 1/100. > Quite possible. I think that teachers union dislike the idea since in science teaching an objective evaluation of whether a good job is done is possible:-) Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same" |