Non-Conservation of Angular Momentum - How does Torque Come into Play?

Okay, here is a rotational motion problem that is baffling me:

We are given an object's (specifically, a wheel's) moment of inertia, an initial rpm, and a final rpm. The question is: What (constant) torque is required to produce the angular acceleration?

No time is mentioned at all, so

(torque) = (moment of inertia)(angular acceleration)

is out. I suspect that I must use angular momentum somehow. However, the book (Schaum's Outline series) provides no specific examples, except in the case of conservation of angular momentum. On the net there are tons of examples of conservation of angular momentum when there is no net torque acting on the object. But I can't find any examples to tie together

(final angular momentum) - (initial angular momentum)

and torque.

This is driving me nuts.

Another Reason to Homeschool II

Glad I'm not in France. I'd like to think that an American audience would do better, but I'm not so sure:


http://view.break.com/335023 - Watch more free videos

Another Reason to Homeschool

Introducing "forgiving" division - one of the latest fads from the wonderful world of the educrats, where constructivist philosophy decrees that constantly reinventing the wheel is somehow nobler and more memorable than instruction in the proper use of tools in the first place. Sure it works, but that in and of itself is no reason to advocate the abandonment of traditional long division.

You could pound nails with a rock. That "works," but you'll never catch a joiner or master craftsman tossing out his hammer and filling his toolbox with various chunks of gneiss.

If you have the stomach, witness the silliness:

One More, for Math Geeks

The singer needs voice lessons, but geeks can overlook that shortcoming:

What Do You Want to Be When You Grow Up?

It's sad that such a concept is deemed almost heretical to the average man in the street, but it's true. Why push everyone into college? Not all high school graduates are really cut out for college, and it is irrational to rack up a ton of debt for something that for most people is irrelevant to success in one's adult life.

Gifted? Oh, Really?

According to a US Census Bureau report, nearly 25% of kids "were in a special class for gifted students or did advanced work in an academic subject." Must be a rather expansive definition of "gifted" - IQ scores of 130+ ("gifted" and "genius" level), being normally distributed, are less than 3% of the population.

Question: If 1 in 4 students are "gifted" or doing "advanced" subject work, why then have SAT scores steadily declined since the early '60's?

I think a lot of the "gifted" labeling is probably motivated by the opportunity to get additional funding more than anything else.

My, How Times have Changed

Last night I watched an episode of Andy Griffith, one of the older ones in glorious black and white. Opie had gotten straight As on his report card, and Sheriff Taylor was so elated that he heaped praises on the boy. The next day at school, however, Miss Crump called Opie forward and apologized, explaining to him that she had made a mistake in transcribing the grades - not only did Opie not get straight As, but he had gotten an F in math. Opie tried to tell his pa about it, but when he came home from school Andy and Aunt Bee surprised him with a brand new bike. Guilt-stricken, Opie declined to ride it, and after other attempts to enlighten his dad, ended up running away from home. Of course, Miss Crump happened to stop by the courthouse and wound up telling Andy the situation. In the end, Andy found Opie and apologized for putting such an undue emphasis on grades, etc.

The thing that struck me while I watched this was how students in the 21st century would have reacted in the same situation. If a teacher had accidentally given the wrong grades to a student, the student and/or the parents would try to leverage that mistake to their benefit and insist on getting the higher grades anyhow, even when undeserved. If the teacher were to hold her ground, the parents would escalate the situation into a lawsuit, or at least threaten to do so. Students are so hung up on grades and scores that they miss the forest for the trees. If they'd concentrate on learning, the good scores would follow. But to focus on GPA constantly fosters an environment where cheating thrives.

By the same token, focusing on learning means that No Child Left Behind wouldn't be a big deal, either. I know that NCLB happens to be a favorite whipping boy of the teachers' unions, but the fact of the matter is that if the kids are learning, they'll do fine. If they're not learning, though, then, yes, NCLB will hang over their and their teachers' heads like a ton of bricks. There has to be some objective, measurable method of determining whether or not kids are getting a solid education built on the three Rs, and NCLB acts as a metric for that. If kids can't read, write, or do arithmetic, then what are they learning?

Cool New Toy

This is one of the things I got for Christmas from my nephew. I've been wanting one ever since I visited this site. I've been practicing on the virtual one all fall, so I am not too bad at the techniques involved, such as adding/subtracting complements. The downside is that now when I use the real McCoy, my fingers feel like little sausages. I suppose agility and speed will come with practice, but I don't feel particularly nimble right now, and the beads seem on the small side.

At least it's not as complicated as some of the scientific calculators that are out now. Half the time if I want to do anything with my TI-89 that involves more than +, -, X, or /, I have to consult the manual to figure out how on earth to do it. There's something to be said for the simplicity of a soroban!

"Heretical" Thoughts

This guy says what I have been thinking for some time. Glad to see that there are some fellow "heretics."

Here is another voice expressing the same concern.

Logical Consequences of Pomoism?

Yesterday we went to my hometown to watch the Memorial Day parade. It was pretty much as it’s always been, except…









…I was thoroughly shocked by the high school band – seriously. Why? Here it was, one of the TWO times in the year that they actually get out and march (well, if you can really call it that; “shuffle” is considerably more accurate) in a parade (the other occasion being homecoming), and they were NOT in uniform. Nix. Zilch. Nada. Just jeans and (matching) t-shirts.







WHAT ON EARTH is that all about? Where’s your pride? Sure, it can get warm in a Memorial Day parade. Sure, some kid will probably pass out. So what? Everyone survives. You mean to tell me you’re too lazy and self-centered to get out of your grubby clothes and put on an actual uniform to march in a parade on Decoration Day as a way of honoring the fallen in combat?










Shiftless brats. The band director that we had when I was in high school would NEVER have tolerated such an attitude. We had too much pride to be slovenly attired like what I witnessed yesterday.











Mr. E., I hope you weren’t watching the parade. Remember your CGHS Trojan Band the way it was………

Ah, that explains it...

If your child is struggling in school, here's a possible explanation. I just wonder how long it will be before the educrats take this idea and run with it. :)

Spoiled by Technology, Part II

This semester I'm teaching a couple of courses at a community college. One of the courses is finite math, which happens to have more than its fair share of using augmented matrices to solve systems of linear equations. Guess who is not fond of using the Gauss-Jordan method to row-reduce a matrix. Thank God, the TI-89 saves me from the tedium of having to solve those things.

Spoiled by Technology

I had half a roll of film in my camera, a leftover from my trip to Korea. Figuring it was about time to finish it off and get the thing developed, I decided to take some pix of the kids playing around the house. Great idea, except I neglected to check some key settings.

Shooting pix 1/500th at f11 just doesn't cut it when your sync speed is 1/60th and you've set the flash for f4.0.

I guess I'm going to get half a roll of rather thin negatives back from the developer...

Teaching Philosophy

(The following is something that I prepared for a job application. It turned out not too bad, so I thought I'd share it here.)

Over the course of my teaching experience, I have developed a teaching philosophy that has proven to be practical and effective, yet retains its intellectual integrity. A major component of my teaching philosophy is based on the so-called Socratic method. From experience, I know that for many students, math appears to be very much like a magician’s sideshow – first we do this, then we do that, and voilà! – out pops a solution. If a student does not follow what the teacher did, or fails to understand the steps taken in solving a problem, then the student stands little chance of mastering the concept, and will at best demonstrate mere competency that is most likely arrived at with difficulty. To minimize this seemingly magical aspect of math, I prefer instead to approach problems from the students’ point of view: Here is the problem, and we have a fairly good idea as to where we are supposed to end up; now, how do we get there, using what we know at this time? Thus, I think out loud for the students, soliciting their input and trying their suggestions. If an approach is suggested which I know will not work, I still play around with it briefly before informing that it will not work, and explaining why it fails. In my opinion, this is an excellent way to teach mathematics: lecture, which is the equivalent of equipping the students with the tools necessary for the task, and problem-solving, whereby the students learn vicariously how to put the tools to use and why we do it in the manner that we do, as opposed to some other way.

Other aspects of my teaching philosophy complement this Socratic approach. I believe that all students are capable of achieving what is expected of them – all students can master the material, given enough encouragement and practice. Thus, I believe that homework is an integral part of a math class, for it provides the student with the practice that is necessary for mastery. But although practice is necessary, it is not sufficient – encouragement is also a key component. All students from time to time will encounter situations and concepts that prove to be challenging to them, but with some encouragement and perhaps a little prodding from the teacher, they can overcome the stumper and press on to victory.

Because all students face a challenge at some point, I believe that it is important for the teacher to take into account the various learning styles that are present in the average classroom, particularly in explaining unfamiliar concepts. Some students learn best visually, some aurally, etc., so the wise teacher utilizes different approaches when it is apparent that students are failing to grasp the thrust of the lesson. The teacher should also foster an open atmosphere where the students understand that no question is too silly, and chances are that if one student has a question, then it is likely that others have a similar question as well.

I believe also that the teacher needs to be able to explain concepts without relying on obscure argot; after all, the goal of teaching is to enlighten, not obfuscate. Cryptic terms and concepts need to be explained clearly before they can be used and mastered with confidence.

Bore Your Kids Day

Tomorrow is "Take Your Daughter/Son to Work" day. Yippee. I'd forgotten about it since I really don't pay attention to these things, but by happenstance today's WSJ was delivered to us, and I read one of the columnists' pieces on the subject. Of course, he had his own take on it (generally negative), but then he posed to his readers the question of whether or not the day is worthwhile.

My answer: It depends. Had there been such a thing when I was of junior/senior high age, it could have been interesting. My father worked for a major company (which no longer exists) which was part of the original Bell family, first in tool and die, but later he moved up to something more akin to an engineering position, doing time/efficiency studies and things of that sort. There was only one time that I recall going to visit his place of employment, and that was when they had some sort of family day on the weekend. I was able to look around and see where he worked and so on, but it really didn't give me any idea (at least, none that I can recall) of what he actually did, or what other types of positions were available within that industry, if not at that particular plant. So, I think that I could have benefited from a visit to his work during working hours and seeing what actually went on there.

Other children could also benefit from a day visit to dad's (or mom's) place of employment, if (no doubt you divined this sentence would be conditional :) it were an interesting or inspiring profession - doctor/nurse, engineer, lawyer, reporter, etc. But how many children would fall into that category? How many parents work at a job where they're bored out of their gourd? How inspiring would it be to spend a day at a place like that? It would provide little incentive to get an education, and the kid would probably come away thinking that being a beach bum sounds a lot better.

Granted, somebody has to do the boring jobs. But most parents have greater aspirations for their children than waitressing (which, I concede, wouldn't necessarily be boring, especially if a lot of alcohol gets served - but even if it gets exciting like that, it would hardly be stimulating or intellectually challenging) or custodial work. Many parents, particularly immigrant ones, break their backs at menial or tedious jobs in order to have enough money to provide a decent education for their offspring, thus giving them the opportunity to have a better life than their parents. I salute such parents; it saddens me when these same kids are clueless regarding their parents' sacrifice, and squander the opportunity.

Rather than have "take your kid to work" day, I would prefer to see the development of some sort of cooperative program between a local high school and the professionals in the community. Not necessarily some work-study type of thing, but more along the lines of a mentoring relationship, or an extracurricular special interest club - something that would allow teens to see how studying x, y, and z are useful (if not necessary) in the field of medicine, engineering, or whatever. I think that that would drive home the relationship between what is learned in the classroom, and what goes on in real life far better than the current crop of dumbed-down textbooks that try to cover everything but teach nothing. I know that I could have benefited from such a program, instead of spending a number of years knowing my interests but never being able to figure out how to utilize them in gainful employment.

We've Come a Long Way, Baby

The other day I was talking with a couple of the kids that I tutor, and the subject of lunch money came up. At least, when I was in K-12, we would have called it "lunch money." Each week we were given lunch money with which we would buy our lunch ticket. Evidently, things are a lot more sophisticated now. Not that kids aren't still given lunch money, but instead of buying a lunch ticket, they give their money to whomever (lunchroom teacher? cafeteria worker? It wasn't clear to me) and then the money is deposited into individual student accounts. To purchase lunch, the student enters his PIN and the amount of his purchase is deducted from his account. I suppose that in some respects it's more convenient than lunch tickets (nothing to lose, and other kids can't horse around and take it from you), but somehow I have trouble imagining a 1st grader actually remembering his PIN from one lunch to the next. A 1st grader is hardly likely to remember to tie his shoes or zip his fly, let alone recall a four-digit number, or however long it might happen to be.

Okay, time for a little trip down memory lane. (Those of you too young to remember, please quietly shake your heads in disbelief if you must, or at least keep your snickers to yourself.)

When I was in grade school, we had the responsibility to purchase a milk ticket (which were blue) or hot lunch ticket (which were pink) at the beginning of the week. It seems to me that milk was 2 or 3 cents per carton (a half-pint), which translated to 10 - 15 cents per week. (I haven't the foggiest idea how much a hot lunch cost; I always brought my own lunch because I had heard rumors that if you bought hot lunch, the lunchroom teacher* would make you eat at least three bites of everything on your plate, and there was no way I was going to survive having to sample spinach or something equally unappetizing.) When it was lunch time, you'd wait in line for your milk (or hot lunch, if you were brave) and the teacher would punch a hole on the appropriate day as you picked up your carton. Initially, in 1st grade I brought my own milk in a thermos along with my lunch; after being unlucky enough to drop my thermos and have the glass tube shatter, I opted for the convenience of buying milk at school.

In high school, we had graduated to a ticketless system; i.e., everything was strictly cash. By now I had outgrown my fear of school hot lunches, so I broadened my menu to include hamburgers, hot dogs, spaghetti, soft pretzels, and pizza. I drew the line, however, at pizza bread; it just seemed like an ersatz replacement for the real deal.

By the time I got to university, the system was far enough behind that we were still using the meal ticket system. Of course, there were other signs & symbols of antiquity: rotary phones in the dorms, punch cards and arena scheduling, students who were lucky enough to bring a computer to school used a TV monitor instead of a CRT - PC's were essentially non-existent and were called "microcomputers" at any rate, connecting to the school computer involved dialing up on the phone and slamming the receiver down into the rubber cups on the modem once you heard the high-pitched computer tone, email was limited to sending to other students who had an account with the university's computer department. Oh, and Pac-Man and Donkey Kong were in...

Ancient stuff? Actually, not that long ago...

*Rumor or not, this seemed plausible to me, because the lunchroom teacher happened to be my 1st grade teacher as well, so I not only knew of her reputation, I had seen it with my own eyes. Not that I was a recipient of her disciplinary ministrations, but I had witnessed it plenty of times with my classmates. I remember one kid who had transgressed in some way; my 1st grade teacher grabbed him by his earlobe and hauled him off to administer justice. Harsh? Maybe, but I can tell you that we didn't have metal detectors in schools, nor did we ever worry about school shootings or other crazy stuff. If only they could clone Mrs. Gable and install her as a 1st grade teacher across the nation, I bet there'd be far less violence happening in the schools, and reading scores would rise...

Mark who?

I honestly wonder what kids are learning in English Lit these days. I'm tutoring some junior and senior high students in English, not because they're stupid, but because their parents believe that extra instruction in reading, composition, and vocabulary would be beneficial to them.

So, I'm starting things off by going through some short stories with them. In particular, we are reading The Californian's Tale, by none other than Mark Twain. Yes, that same Mark Twain who wrote (among numerous other things) such classics as Tom Sawyer, Huckleberry Finn, The Prince and the Pauper, and A Connecticut Yankee in King Arthur's Court. Granted, I myself have not plumbed the depths of Twain's writings, but at least I have read the first three just mentioned.

However, upon questioning my students if they know who Mark Twain was, all I get are mumblings and blank stares. It's incredible that the name of one of the giants of American literature should elicit no other reaction than a shrug of the shoulders and an "I dunno"! (To give credit where credit is due, one student did mention, "I think I read something of his once," but when pressed for the title of the reading, couldn't provide any clue.)

They know nothing about Mark Twain - what he wrote, when he lived (not even the general time frame), where he was from, what his real name was - NOTHING. It's inconceivable to me that any American student can get through junior (let alone senior) high without possessing the foggiest idea who Mark Twain was, without reading even an excerpt from one of his numerous writings. I remember reading Huckleberry Finn in fifth grade; don't tell me that Twain's writings are inaccessible to any junior/senior high student of at least average intelligence.

I think it's safe to say that if Mark Twain is a stranger to American students, then James Fenimore Cooper, Washington Irving, Nathaniel Hawthorne, Herman Melville, and Edgar Allan Poe have hardly fared any better.

What are they learning, indeed? PARENTS! An "A" in English doesn't mean that your junior or senior high school student is actually learning anything....

"...But Hey, I've Got Good Self-Esteem!"

To celebrate the new year, we decided to go up to Wisconsin Dells and stay overnight at one of those hotels that has an indoor water park. We enjoyed ourselves tremendously, as did our dd. There was just one fly in the ointment: it was the last day before the kids went back to school, so, as you might imagine, there were plenty of under-18 personages running around.

Now, as anyone who knows me can tell you, I like kids. Small fry don't bother me. But when I see some of the older kids copping an attitude, that is a major turnoff. Unfortunately, a number of the pre-teen/teens suffered from the delusion that the facilities existed solely for themselves, and that rules are for lesser beings: "Hooray for me, to heck with you, and get outta my way" (as my father would put it). They would shove past you climbing the stairs to the water slide, evidently wholly ignorant of vocabulary as "please excuse me" or "sorry," not to mention the utter foreignness of actually waiting in line for one's turn. In a circulating water lap where one could grab a tube and float lazily past replicas of Mayan ruins and man-made waterfalls, these kids would jostle past you and anyone else in their way in their quest to see who could finish first. (Hey, kid, if it's that boring to you, go find something more exciting.)

So I found myself thinking about the whys and the wherefores of these little barbarians' lack of manners. Where are the parents? Why have they apparently abdicated their responsibility to teach their kids that they are not the focus of the universe, and hence need to learn to give consideration to others?

Where are the teachers? If they let their pupils get away with that type of behavior, then I don't see how they can accomplish anything remotely resembling instruction in the classroom. I suppose the educational powers that be figure that teaching things like "self-esteem" and undermining traditional views of marriage and human sexuality are far more important than quaint, outdated concepts such as social graces. (Of course, being a private tutor, I can tell you what else the kids are not learning in school - math, reading, vocabulary, science, for starters...but that's another story.)

Where are the Sunday School teachers? In all fairness, probably most of the kids have never darkened the doorstep of a church, but I fear that those who have are more likely to learn about Veggie Tales than the Golden Rule. (I've got nothing against Veggie Tales. My three-year-old likes them, they're entertaining, and the messages are positive. They're just not substantive enough to be Sunday School material, really.)

This selfish attitude reminds me of some articles about so-called "indigo children" I read on the Internet several months ago. (I wish I was making this up, but I'm not, unfortunately.) Judging by the description, a generation or so ago, these so-called "indigo children" would have been unhesitatingly labelled "brats," but now they're simply assumed to be the next stage in "human evolution." Even more appalling was the recommendation that these brats be allowed to develop their brattiness unfettered by parental restraint (lest it damage their psyche and thwart their evolutionary destiny, y'know).

Call me old-fashioned, but there's no way I'm going to let my child grow up to be an ignorant, spoiled brat. She deserves better than that.