Physics 125

Final exam scores

2009-05-07T02:24:00.003-05:00

Your final exam scores are on moodle ...

The final course grade posted is basically correct, but subject to an audit of my master spreadsheet. Very few were on a grade boundary (either +/- or a full grade) as it turns out, so probably nothing will change, but I want to be on the safe side and check everything a few more times.

Now is a good time to check that your HW, lab, and quiz grades seem correct. If you are curious about what grades you are missing (e.g., HW not turned in), send me an email.

Final exam breakdown

2009-05-07T01:51:00.004-05:00

Individual final exam scores will be on Moodle imminently. Must make one more check of grading ...

Final course grades will be posted sometime tomorrow afternoon. I need to do a thorough review of everything before I'm willing to posit final final grades, and carefully audit everything. You can calculate from Moodle what you should receive, and there is a 99% chance you will be correct. Keep in mind Moodle does not include random bonus points I have given over the semester, for instance, and for this and other reasons the Moodle grades are not 'official.'

Incidentally, the overall course grade is a very complicated case. You know, a lotta ins, a lotta outs, a lotta what-have-yous. Mostly when you are on the narrow borderline between grades ... there are often some very tough calls to make.

Let it suffice to say that I usually err on your side if there is a chance for ambiguity, but it is rarely (rarely) necessary. Strictly by the numbers in the end.

e-homework chaos

2009-05-07T00:43:00.001-05:00

A nice post about how having emailed homework can suck.

Pretty much everything she mentions has happened this semester, and then some ... but it all worked out in the end.

Also, she missed a lot of other chaos-inducing problems, like email addresses that give no hint as to the sender's address coupled with no discernable name within the attachment. Thanks to what I think is better-than-average handwriting recognition on my part and good email search capabilities, this was not much of an issue this semester.

In other news, the finals are graded. I have not tabulated the results yet ... probably in another couple of hours, I will post here when I have results for you to see.

Final Exam

2009-05-05T09:26:00.003-05:00

Your final exam is here, if you want to look back at it ...

Also, moodle is now up to date with everything except the final exam. Labs 9, 10, and 11 were from the rocket competition:

L9 = competition performance
L10 = quality / correctness / cleverness of code
L11 = quality / cleverness of the physical setup and measurement system

FYI, the grading breakdown (weighting, number dropped, etc.) can be found here.

Moodle

2009-05-05T02:23:00.003-05:00

HW 12 grades are now up on Moodle. The only grades missing are from the rocket launcher project, which counts as 3 lab grades.

Excepting the 3 rocket grades, you have 8 lab grades in so far. I will add in the 3 rocket grades (performance, code, and hardware) and drop the lowest 2 grades overall (for a total of 11 lab grades). I should have this done late Tuesday or early Wednesday.

After you finish the final exam tomorrow, you can check with me to see that your grade distribution is accurate - e.g., missing homeworks and labs. If you don't see this in time, send me a short email and I'll let you know what grades I'm missing from you to make sure everything seems to be correct.

I will probably have final grades done by Friday; I'll post here when I have everything finished.

Formula sheet

2009-05-05T02:11:00.001-05:00

Here it is.

Draft anyway; some proofreading remains.

Review Session TONIGHT

2009-05-04T09:45:00.003-05:00

Room 203 Gallalee, the usual classrom, 6-7pm.

Come bearing questions ...

Final Exam

2009-05-02T02:27:00.003-05:00

One of you asked about the final exam details. Below is what I said.

The review session will be Monday evening, I'll post here when it is finalized. I'll also provide the formula sheets, probably on Sunday, along with more detail. It will be easier than any of the other three exams I gave ...

It is going to be a larger number of much easier problems, much like the example problems in the chapters. Only chapters we covered in class are on the exam, and nothing we covered after exam III is on the exam.

It is going to be something like 8-10 fairly easy problems that you need to solve in about 15 minutes each, rather than the 4-6 hard problems that take 30 minutes you had on the previous exams. You will have a choice of problems, so it is reasonable to skip over a couple of chapters and just not choose problems related to them.

My suggestion would be to try to solve the sample problems without looking at the solutions at first. Basically, the exam will reward knowing the basics really well. I will try to make the problems very similar to the level of practice problems. After that, I would try the problems on the sample tests I posted - mostly easier problems than we have been doing.

You'll get a formula sheet which is fairly comprehensive. I'll try to post it as soon as I can, but it might be Sunday before I get it done. It will be a combination of the formula sheets from the first three exams. You can bring in two sheets of paper with your own notes.

We made the news ...

2009-05-02T02:23:00.002-05:00

Video of the contest on the Tuscaloosa News site.

UA News writeup.

And, Mr. Cecil is on the front page of the "B" section of Friday's Tuscaloosa News. Very cool. Try to save him a copy of the paper if you can :-)

Reminder: no recitation today

2009-05-01T09:33:00.002-05:00

Also, I will hold a review session Monday evening some time. Still working out the details, I'll post here when everything is settled.

Reminder: code submission

2009-05-01T09:09:00.002-05:00

Each team owes me code ... soon.

Don't worry about dependencies, libraries, etc. I'll figure it out.

Rocket Contest

2009-05-01T00:45:00.016-05:00

Well, I was pleased, and had a good time :-) I thought it went well, and you all did a great job. The visitors were pretty impressed with what you were able to come up with, and in particular the variety of solutions presented.

By the way: no one will come out of this with a bad lab grade, I was impressed all around. Even if you didn't get as many 'hits' as you would have liked, it was clear you all had solid approaches and took the task seriously, and that's worth a lot.

Currently, I'm uploading many photos and some video from today, but I'm not quite finished yet ... I'll post some links here when it is finished. Keep your eyes on the Tuscaloosa news, they may run a story based on the video and pics they took today.

Also: I've decided you can keep the launchers, sensors, and laser pointers - your lab fees more than paid for them, and at this point you put a lot of work into the customizations. I do need the voltmeters back if you still have them though ...

In the mean time: here is (1) a UA news bit, (2) a short video of a successful shot, thanks to Marcy Huey's fine camera work, and (3) a listing of several other videos, including team Red Scare's propaganda.

(All videos are AVI straight from my camera; editing and conversion to mpeg should happen this weekend I hope.)

Last-minute things for the competition

2009-04-29T23:21:00.005-05:00

Last minute preparations and information ....

Things: Tomorrow, I will bring the following items, at least:

USB extension cable
tape measure (verify ceiling height, etc)
camera
soldering iron (sensor repairs)
stopwatch (elapsed time between shots)
target

What to bring: The launcher (duh), position sensor, and the computer running your calculations. If you need a computer for tomorrow, you'd better let me know soon. Like right now.

Press: It is not clear if press will come or not - they won't know themselves until the last minute. They have been invited, so we'll see what happens. If they do show up, it would be nice if a few of you were a bit early to the competition so they can ask you a few questions. Obviously this is optional, but the basic point is, 'show up early, and there is a chance you'll be interviewed.'

Visitors: There are going to be a number of random visitors tomorrow. Pay them no mind, go on about your business :-)

Location: Shelby L107. This is not the same as 107, a lecture hall you may have had classes in.

Directions: from the rotunda entrance, go left. Continue down the hallway until you reach the breezway. Go through it and into the next hallway. At the dead end, turn right. L107 is on your right. I will have a few signs up to guide you.

Timing: We might be done by 12:30, it is hard to predict. We will not go beyond the normal class period.

Grading-related: Remember that you need to turn in your source for the trajectory calculations. Please try to do this by the end of Friday.

Ok ... that is all I can think of right now. The contest will be pretty relaxed, but we will have to be efficient - with 5 teams and multiple shots, it will take a while.

Physics Majors on Facebook

2009-04-29T14:00:00.001-05:00

Join us.

Quiz 8 & 9 solutions

2009-04-29T01:44:00.005-05:00

Well, answers anyway. Almost everyone aced quiz 9 (thermo). Quiz 8 was not quite so great ... but I think now the answers will be clear to you.

Moodle update coming shortly (give me like 30min) so you can see your quiz results.

Exam III solutions

2009-04-29T01:10:00.001-05:00

Here you go. Let me know if you find any errors.

Physics Majors event

2009-04-28T22:05:00.001-05:00

Just FYI, since a number of you are physics majors ...

---

All PHYSICS MAJORS!!!

Do you actually know other physics majors?? Yeah, that's what I thought. So come to the meet AND greet.

FREE FOOD! Yes, completely free. In fact, it will even be surrounded by nerds. So come.

DETAILS:
Who - YOU....hopefully...
What - Meet the other people who share your uniquely awesome interests
When - FRIDAY, as in THIS FRIDAY of dead week. which is May 1st, just fyi. 3:00-5:00pm
Where - Room 109 in Gallalee (obviously)
Why - because Tara and Ted were upset that we didn't know all of you

So, it'll be awesome, especially once you get there :)

-Your Fellow Physics Majors, Tara and Ted - and kind of the Society of Physics Students, kinda -

Old PH105 Exams

2009-04-28T01:56:00.002-05:00

I put up some old PH105 exams for you to look at - some with answers only, some with solutions.

They are easy problems compared to what you've been doing, but good practice nonetheless. For the final it will be advantageous to be able to quickly solve a larger number of straightforward problems, as opposed to our usual exams where you have to solve only a few tough problems.

Tuesday's class

2009-04-28T01:30:00.003-05:00

Today we'll go over some review questions, and spend an hour or so practicing for the rocket competition on Thursday.

Also, I had completely forgotten about Exam III solutions until one of you reminded me in the comments ... I'll get on that and have something for you by Thursday at the latest, along with solutions to the example problems from last week. The end of the sememster is proving a bit more painful than expected, so I am a bit behind ... apologies.

I have put up some very silly flyers to advertise our little contest. If you feel so inclined, you can do some of your own advertising as well. A number of faculty and staff members have expressed an interest in coming to watch the competition, mainly because they think what you've been up to is very neat. Probably, they are jealous.

(I may have mentioned this to the University Relations office. There might be local press.)

Finally, I'll post directions to L107 Shelby soon. You can find a handy map here. Note that you are going to L107, which is not the same as plain old 107. (Grab the 'emergency evacuation plan' map, it is actually much clearer. And possibly quite relevant, one never knows.)

Common Misconceptions

2009-04-26T11:07:00.004-05:00

Nice link courtesy of Alex.

I liked this bit at the end:

"A telling comment on the issue of fairness in teaching elementary physics: Two students asked if I was going to continue asking them about things they had never studied in the class."

The answer is always this: HAHAHAHA yes.

(I am at least mostly kidding. There won't be any material on the final that we didn't cover in class, but there will be relatively simple situations that are new ... but situations which can be handled straightforwardly with what we covered in class. No surprises.)

Quiz tomorrow (Friday)

2009-04-23T22:29:00.002-05:00

Reminder: there is a 5-question multiple-choice quiz on Ch. 18 tomorrow.

The content of the quiz will be restricted to the sample problems in Ch. 18 - if you can do those, you are good to go.

In addition we'll go over some practice problems for the final (the ones I put on the board today).

Today's class ... probably

2009-04-23T01:40:00.004-05:00

I am mulling over a change of plans. On one hand, we should do more thermodynamics. On the other hand, you will all end up taking it again anyway ...

So here's my thought: if you agree to do a bit of reading on your own and take a short multiple-choice quiz on Ch. 18 on Friday, we'll spend tomorrow doing final exam review instead. Nothing we covered after Exam III is on the final exam, so this is a reasonable gamble for you to take, I think.

Anyway: tomorrow you have a choice - lecture on heat and thermodynamics, or do practice problems for the final. Since our PH125 Deathwatch is in its final stages, here's what the rest of our time looks like:

This week:
Thurs: practice or thermo + concept test + rocket testing
Fri: pending your vote for Thurs, possibly a thermo quiz. Post-mortem on the concept test (i.e., where are you as a whole having the most trouble). After thinking about Crito's comments & link, I'll also point out the ones I thought were tricky and why ... where does intuition seem to fail?

Dead Week:
Tues: final exam review, dry run for rocket competition
Thurs: rocket competition
Fri: no class

Thursday's class

2009-04-22T01:19:00.002-05:00

Thursday, we'll be doing our requisite post-assessment. Remember that concept test you took at the beginning of the semester? Basically, we'll take it again and see if you learned anything :-)

It should take about 20min, and there will be grade-related incentives for doing well.

We'll also go over a bit more thermodynamics (heat and energy), and leave some time for you to do some 'practice shots' for the rocket competition.

Evaluations are today

2009-04-21T11:02:00.001-05:00

If you were planning to stay home this morning ... we are doing course evaluations during the second half of class. FYI.

Last HW set

2009-04-20T10:12:00.001-05:00

Here it is.

As I noted before, this one is optional - you don't have to do it, but if you do, it can replace your lowest non-dropped homework grade. Also useful for preparing for the final exam ...

Rocket launcher code

2009-04-16T12:25:00.001-05:00

Linux kernel module to control the launchers. Should be portable ...

Update: code for OS X here. Pretty readable & hackable. You are not by any means required to include rocket launcher control in your code, this is just in case you're interested in trying it for 'fun.'

Exam III details

2009-04-16T02:07:00.007-05:00

(Update: if you checked Moodle within the first ~10 minutes of my posting this, I may have been updating the overall grade calculations at the time. Anything after 02:35 is accurate.)

I finished grading your exams, albeit under somewhat savage time pressure these last days. That means I haven't had time to process the results very much, but your raw scores will be available on Moodle in the next half hour or so. Anyway, the results:

Average: 73%
Std. Dev: 14%
Hardest questions: 2,3,4

Based on these numbers, I will scale it a bit. Probably, this will mean adding something like 5-7% to your test grade, but I haven't decided that yet. I will scale it such that the class average is at the C+/B- border with a favorable distribution. Details of this should be clear by Friday ...

Despite the averge being a little lower than I had anticipated, I am happy with the results, having seen how you went about the problems. By and large, you know what you are doing, and it was mainly time pressure and simple things that tripped you up. We'll go over the solutions in detail today in class. As a peace offering for giving another bastard exam, we will also devote a good amount of time to rocket targeting and such things and less time to lecturing.

Random plots for your perusal:

Exam III grading

2009-04-15T00:45:00.002-05:00

I hope to have the exams graded and back to you by Friday ... I would say Thursday, but I have a visiting grad student coming in tomorrow.

In any event: you'll have them before the weekend if all goes according to plan. Don't freak out, it looks pretty good so far. I will scale the exams if necessary.

Most likely on Thursday we'll go over the solutions in class.

Exam III

2009-04-14T11:13:00.001-05:00

Here it is. I'll try to have solutions out by the end of the week.

Exam III is IN 2 HOURS

2009-04-14T09:05:00.003-05:00

Seriously, people have forgotten before.

Bring a calculator. And writing implements. You won't need anything else.

Have some coffee. Bring music (with headphones) if you think it will help.

Don't forget that you can ask me questions during the exam, and I am somewhat likely to give helpful advice.

Today's office hours

2009-04-13T10:28:00.004-05:00

Today I have a meeting that cannot be avoided, and it overlaps the posted office hours ...

If you want to come by today, I'll be in my Gallalee office from 5pm until the review starts.

Solutions to Friday's quiz

2009-04-13T01:51:00.002-05:00

Here is Friday's short quiz, and a solution key.

Exam review session

2009-04-13T01:21:00.002-05:00

How about 7pm, Monday 13th April, in our normal classroom.

I'll go over some example problems and more details on what precisely will be covered. Come with questions.

HW 12 solution

2009-04-13T01:20:00.001-05:00

Here you go. Let me know if you find any mistakes or have any questions.

Formula sheet, Exam III

2009-04-12T21:17:00.003-05:00

Here you go.

Working on the HW12 solutions now, I'll post here when they're finished.

There will probably be a review session tomorrow (Mon) evening at 7pm ... I'll decide tonight and post details.

Studying for the exam ...

2009-04-11T20:31:00.001-05:00

I hope to have the formula sheet for the exam and the solutions to HW12 posted by mid-afternoon tomorrow (if not sooner).

Last problem

2009-04-10T21:58:00.002-05:00

the possible modes of the string have

f = (n/2L)sqrt(T/u)

where n is an integer, L is the length of the string, T its tension, and u the density. You know T=mg, tension is provided only by the hanging mass. You also know f is fixed by the resonator attached, f=120Hz. The only variables are m and n.

If the two given masses m1 and m2 work, but nothing in between does, then they must be adjacent harmonics - one is n and the other is (n+1).

Plug that into the above equation separately for both masses, set equal, and you can find n. Once you have n, you know everything in the equation above except u ...

Homework 12

2009-04-09T22:34:00.001-05:00

Remember, today's homework can be handed in as late as tomorrow night without penalty.

Checking your code

2009-04-09T14:45:00.007-05:00

In case you want to check that your code is working ...

If you use the drag equation


F_d = \frac{1}{2}\rho C A \vec{v}\cdot\vec{v}

with starting parameters


v_x=31\,\text{m/s} \\
v_y=35\,\text{m/s}\\
m=0.046\,\text{kg}\\
A=0.00143\,\text{m}^2\\
\rho=1.225\,\text{kg}/\text{m}^3\\
C=0.25

then you should get a range of 126 meters over level ground (and 221 meters with C=0, i.e., no drag).

16.25

2009-04-08T20:53:00.003-05:00

You can find the velocity of a wave at any point along the string if you know the tension and linear density. At any point along the string, the tension is provided only by the rope below that point - you can't push on a rope.

Finding the time is handled just like the last problem in HW10 - t is the integral of dy/v(y), with the limits being the two ends of the rope.

16.34

2009-04-08T20:50:00.005-05:00

The latter parts of this question will make more sense after tomorrow's lecture, if they don't from reading the chapter. To get you started:

The average power transmitted along the string is


P = \frac{1}{2}\mu v \omega^2 y_m^2

Here you don't know the velocity, but you can relate it to the tension and linear density.

If you superimpose two equal-amplitude sine waves together of the same frequency (so kx-wt is the same for both), but they differ only by a phase phi, the resulting wave is given by Eq. 16-51:


y(x,t) = \left[2y_m \cos{\left(\frac{\varphi}{2}\right)}\right]\sin{\left(kx-\omega t + \frac{\varphi}{2}\right)}

The amplitude then depends on the relative phase as well as the amplitude of each wave. If the waves are in-phase, the total amplitude is just double, but if they are 180 degrees out of phase, everything cancels.

Thursday's lecture

2009-04-08T18:42:00.002-05:00

Ok, continuing with waves (Ch. 16/17) has won the poll ... so that's what I will talk about tomorrow.

That implies you should look over Ch. 16 and 17 before class if you can.

Standing waves in your shower

2009-04-08T10:43:00.000-05:00

Important application of waves.

Research Work

2009-04-08T02:36:00.002-05:00

If you like coding, and want to pick up some research work, let me know. Prof. Williams is in need of students to help out, particularly those who know some Java (though good coding skills are generally valuable, you can pick up the Java you need).

Cool factor: her experiment is a giant neutrino detector in Antarctica, see link above. (Pun intended.) Very exciting work, and you would have a chance to make a real contribution to a world-class international research project.

Let me know if you're interested, or contact Dr. Williams directly (via link above).

Current Grades

2009-04-08T02:15:00.002-05:00

Moodle has been updated, your grades for HW10 and labs 7-8 are now there. Everything except HW11 is now up to date.

HW11 should be added by the end of the week, and HW12 over the weekend so that your grades are current going into next week's exam.

(FYI - Lab 6 = project memo; Lab 7 = sensor calibration; Lab 8 = group talks)

Thursday 9 April 2009

2009-04-08T02:02:00.001-05:00

By the way: short quiz on Thursday. It will not present a problem if you have read Ch. 16.

Really, it will be easy. Just a heads-up.

Even-numbered problems for this week

2009-04-07T21:46:00.003-05:00

Numerical answers for the even-numbered problems this week:

Due tonight:
15.24 x < 0.23m
15.56 T~2.0s; 18.4 N-m/rad

Due Thursday:
16.34 10W; 20W; 40W; 26W; 0
16.60 0.846 g/m

Random hints:

15.111 First, for the linear acceleration, you can always just apply the center of mass equations:

m a_com = F_net

Even though rotation is involved, the center of mass stuff still works.

For the second part, you want to find the net torque to get angular acceleration. You have a force F applied some distance x from the point at which the bat is held (point O), and that's it. The distance x is 2/3 of the length of the bat, given. This torque must equal the angular acceleration (alpha) times the moment of inertia about the end of the bat (so (1/3)ml^2).

Finally, if the bat is rotating after the hit, the angular acceleration implies that the tips of the bat have an additional acceleration in the tangential direction. If no one were holding the bat (or if it is held lightly, as the problem states), the rotation will just be about the center of mass. The tangential acceleration at the ends of the bat has to be (alpha)(L/2) in that case. In the end, this acceleration due to rotation acts in the opposite direction compared to the acceleration of the impact of the ball itself. At the "sweet spot" these two cancel exactly, and you shouldn't feel anything when you hit the ball - if you hit anywhere else, it 'stings' because of the net acceleration at your end of the bat.

In other words, there is (say) a forward acceleration due to the force of the ball hitting the bat, and a backward acceleration at the hands due to the resulting rotation. You'd like the two to exactly cancel for your force to be used most efficiently, which is just what happens at the sweet spot.

Thursday's class

2009-04-07T21:35:00.004-05:00

So I'm torn about what to do on Thursday. Therefore, I'm going to let you vote - we can continue with what's in Ch. 16 & 17 (which is probably easier) or do one of two other topics which are a bit more challenging. All three are very relevant topics you *will* see again, so in that sense there is no wrong answer ...

We should continue on with wave motion, but we did cover enough that we could pick up the missing bits during dead week - what is left is mostly pretty straightforward. I suspect that if you read the rest of Ch. 16 and parts of Ch. 17 you can pick most of it up on your own - there is not a huge amount of depth there.

We could also go a little deeper into resonance, which we only touched on. This would involve looking at driven oscillations and expanding our investigation of damping. I think this option is more challenging, but probably a bit more fun.

A third option is to look at coupled oscillations. This is not unrelated to the outstanding material on standing waves, and would get into things like synchronization of oscillators, the speed of sound in materials, and Fourier analysis of complicated waves.

Only the first option is really covered in the textbook; none of these three would show up in any serious way on the final. Vote in the poll at right if you have a strong interest one way or another; I'll lecture on whichever topic has the most votes as of Wednesday evening.

Hint on the 2nd homework problem

2009-04-07T21:27:00.002-05:00

When you have the torsion spring connected to the pendulum, you don't have any sort of simple equation you can use any more ... you have to just add the torques up.

First, you have a torque due to the weight of the hanging deal, something like (weight)(radial distance)(sin of inclination angle) if you're not into vectors. That pulls the thing back to equilibrium.

The torsion spring provides a little 'kick' in the opposite direction to keep it going. The torque provided is just proportional to the angle, (kappa)(theta)

In total you have then (weight)(radial distance)(sin theta) - (kappa)(theta) = net torque. The net torque must be the moment of inertia times alpha, the second derivative of angle with respect to time. If you use the low-angle approximation sin(theta)~theta, you can recover an equation for simple harmonic motion: angular acceleration is (omega)^2 times angle.

Twitter

2009-04-07T13:52:00.002-05:00

The poll indicates that you are not wild about Twitter ... which I can buy.

For that reason, I won't post anything on twitter that isn't also posted here. That doesn't mean I won't post anything to twitter, just that you won't miss anything essential by not following it.

Today's bit of randomness

2009-04-07T10:33:00.000-05:00

Physics is good for anything. Anything.

Exam III

2009-04-07T01:42:00.003-05:00

As it turns out, you have an exam one week from today. The format will be much like the last exam - you will have a choice of problems (e.g., solve 5 out of 8), you can bring a formula sheet, you have 2 hours.

The exam difficulty will be somewhere between the homework problems and the example problems in the book (see below) - not as difficult as the homework (though similar to the non-bastard problems), but harder than the example problems. More details, including sample problems, will follow.

The topics covered are:

10.6-10 Rotation
11.2-4,6-11 Rolling motion, Angular momentum, torque
13.2-8 Gravitation (excluding central force laws, only the stuff in the text)
15.2-9 Oscillations and simple harmonic motion
16.2-8 Waves, pt. 1

Basically, chapters 10, 11, 13, 15, and 16, but not all sections are included. Owing to Honor's day this Friday (no class!), there will not be much time for review. Studying the homework solutions and example problems in the text will serve you well. I'll be online most of the weekend and available Monday before the exam (13 April) most of the day for questions.

There will be roughly 2 questions from each from:

Ch. 10-11
Ch. 13
Ch. 15
Ch. 16

If you have been understanding the homework problems, you will probably be fine.

Tomorrow's class

2009-04-06T19:31:00.002-05:00

(1) Waves: read chapter 16 (or at least skim it)
(2) Problem-solving: homework for this week, more harmonic motion
(3) More rocket madness

Numerical answers

2009-04-06T09:28:00.001-05:00

Preaching to the choir.

HW 11 Solutions

2009-04-05T16:41:00.003-05:00

Here you go. They need some proofreading, but they are basically complete.

Note that for the first problem ScienceWorld already has a great solution up, so I just linked to it.

HW 12

2009-04-04T12:53:00.002-05:00

Homework 12 is out.

Problems due Tues 7 Apr: 15.24, 15.56, 15.111
Problems due Thurs 9 Apr: 16.25, 16.34, 16.35, 16.60

We'll spend plenty of time during the week going over these problems before they are due.

Keep in mind that there is no class on Friday for Honor's day.

Homework via email

2009-04-04T12:20:00.005-05:00

FYI, I've created a separate email account just for homework ... since my inbox tends to get flooded when homework is due.

I mostly plan on using this for next semester, since we are already nearly done and old habits die hard. It is active right now, and I will be checking it ... and it would make things more efficient for me if you sent your homework to this address.

However, you can keep using the normal email address for the semester if you would rather, it isn't a problem.

Today's recitation

2009-04-03T09:44:00.002-05:00

Today, we'll have one more presentation, if all the group members are around ...

After that, we'll work on homework problems - both the ones from last night, and the ones due tonight.

HW10 solutions

2009-04-03T01:44:00.003-05:00

Here you go, all but the last one. Hope to have that solution out over the weekend ...

HW 11: 15.106

2009-04-02T18:37:00.003-05:00

Problem 15.106
a) Translational - 1/16
b) Rotational - 1/32
c) it is a proof ... show that acceleration is proportional to -(const) times position.

HW 10 solutions

2009-04-02T01:57:00.003-05:00

Sigh, I only have the first two problems done so far ... I will be working on them tomorrow and hope to finish them up. Here you go.

At the very worst, I will scan my hand-written solutions tomorrow

Following twitter updates, if you're in to that sort of thing

2009-04-01T20:33:00.007-05:00

I am putting out some homework hints via twitter now, just as an experiment. You do not need a twitter account to follow these updates.

(1) the twitter updates will also be mirrored as my facebook status. You can look at my wall on facebook and see the same stuff.

(2) go to http://twitter.com/pleclair periodically

(3) get an RSS feed of my twitter updates, then you can read them in your aggregator of choice. You can get a facebook application to bring RSS feeds to your facebook homepage, fyi.

(4) (update:) follow the little twitter-box on the right side of this page ... type "pleclair ph125" in the box and hit "set."

One obvious question is why bother with this. I don't know, actually - it may not be worth the trouble. My thoughts:

(a) it is easy to follow twitter updates on a mobile device (if you have enough text messages in your plan). this means you can get HW hints and stuff without having to be near a computer.

(b) it takes me like 5 seconds to make a twitter post, whereas even on the blog I tend to spend 5-10min or so composing a post. If it is easier for me, I am likely to do it more often (even under savage time pressure), and the more help you get. (The reason I switched to a course blog in the first place was speed & frequency over static web pages.)

(c) On the other hand, having this blog is probably plenty already. I may be overthinking this problem, or going toward too many channels of information.

Physics scholarships

2009-04-01T13:11:00.002-05:00

If you are a physics major, it is not too late to apply for a scholarship.

Specifically, the E. Scott Barr scholarships have not yet been awarded. Tell your friends.

Twitter

2009-04-01T10:44:00.003-05:00

So, I am on the twitter (@pleclair). I was thinking lately it might be useful for posting quick updates for class, e.g., HW hints or notifications of new assignments. (Though I joined for other reasons, mainly because all the cool kids were doing it).

Would this be a useful way to disseminate small bits of course-related info?

(N.B. - it is easy to use twitter to update your facebook status and vice versa. Joining is not the time sink I thought it would be.)

HW11

2009-03-31T22:26:00.003-05:00

A little later than hoped, but here is HW11. Based on what we covered today, and sections 15.1-15.4 in the textbook, you should now enough to do all but 15.63 already. We'll go over some of the first ones in class on Thursday. Text-only version of HW11 below.

Problems due by the end of Thursday, 2 April: 15.26, 15.37

Problems due by the end of Friday, 3 April 15.55, 15.63, 15.106

HW11

2009-03-31T01:33:00.004-05:00

Homework 11 will come out some time later today (Tues). They will all relate to Ch. 15 in your textbook. If you want to get a jump, read through Ch. 15 and study the example problems. This week's homework will not be quite as bad as last week's ...

As I mentioned earlier, there are no problems due this week until Thursday, since I'm asking you to give talks later this week.

Talks for Thurs/Fri

2009-03-30T23:01:00.004-05:00

Thursday and Friday of this week, I would like each group to give a short oral presentation on their progress with the rocket project so far. A few formal details:

It is a group presentation - designate a speaker, or take turns. Either way.
Minimum 10 minutes, maximum 15 minutes per group
Powerpoint/etc are not required but may be used if you like.
We will start on Thurs and finish these on Fri. Pseudo-random numbers will choose your presentation order on Thurs.

As for the content, I would mainly like to see you present your basic approach to the assignment, where you are now, and what you think you still need to do.

What is required for the project?
What experimental quantities must be determined, and what is your progress?
What parameters must be controlled, and what is your approach?
What are the relative errors & their sources?
How will you determine the trajectory/angle at launch time?
What problems are still outstanding?
What solutions are you still working on?

I'll discuss this a bit more tomorrow, but hopefully you get the idea. This is really just meant to be a reasonably informal (but not too informal) status report, like an oral version of your memos, updated with all your recent progress.

You can keep the talk fairly general in some respects - I am not asking you to give all your secrets away to the other teams, but I do expect you to give concrete statements about what you have done. For example - quoting your launch velocity and error or discussing the algorithm you are using for your calculations is fairly general. Giving away your trick for highly accurate positioning of the turret or optimizations to basic algorithms is not necessary.

Grade-wise, this will count as a lab.

Tomorrow's class

2009-03-30T22:57:00.004-05:00

Tomorrow, we will begin Ch. 15, "Oscillations," and continue with this material for the rest of the week. Start reading :-)

We will defer Ch. 14 on fluids until the end of the semester, for two reasons. First, the material is a bit fluffy at the level presented in the text. It will be nicer to cover this during our last week, when the PH125 Deathwatch begins. Second, I think it is more logically consistent to move on to oscillations now that we have covered all the core topics in Mechanics.

Next week, we'll begin Ch. 16, "Waves I" ... and the week after that is Exam III (April 14).

HW11

2009-03-30T07:56:00.002-05:00

HW 11 will come out later today, but there are no problems due until thursday.

That is, I'm giving you the day off from homework tomorrow so you have some time to work on your presentations for Thursday & Friday. I'll post details about the presentation requirements later today to help you get started.

Friday's class

2009-03-27T01:23:00.004-05:00

We'll delay harmonic motion until Monday. Tomorrow we will spend some time solving homework problems, and a little bit of time discussing the rocket project and your (informal!) presentations for next week.

For the rockets, I'll sketch out some algorithms and pseudo-code you can use to get the trajectory and then find the launch angle (some of you have already done this). There will be extra points for particularly clever solutions, so it is worth some time to optimize your calculations. I heard talk of pointers today, and it pleased me :-) I should mention that spiffy user interfaces and graphics are not necessary, we would rather focus on cleverness of calculation and efficiency for now.

I will also introduce you to the position sensors you'll be receiving next week (one per team) that you can use to determine the target's range and height.

Homework due at what time?

2009-03-27T01:03:00.004-05:00

So I have said that the homework is due at the end of the day formally, i.e., 11:59pm on the day in question. That is still true. There are 'grey areas,' however.

Less formally, it will not be considered "late" if I am still awake after that time. Tonight that means you have about another hour or maybe 90 minutes. In general, 1-2am is a reasonable bet. If you're staying up until 2am doing homework, that is hardcore, and I'll give you some leeway ;-)

Minimal points are taken off for submissions arriving before I begin grading the homework, usually a day or two after the due date. Things happen, you get busy. Don't make it a habit.

Submissions after I have already posted the solutions online are taken on a case-by-case basis, but will receive some credit for at least bothering to copy the solutions. Learning by osmosis can work sometimes.

The message here is again: always turn it it. It is never given zero credit.

HW 10 question 9

2009-03-26T22:15:00.002-05:00

Updates to the hint to fix the glaring error. (with the proper link this time)

I might try to revise it a bit more to make it less terse ... I'll post here if I get that done.

Even-numbered problems for this week

2009-03-26T21:40:00.007-05:00

13.16 3e-10 N
13.68
a : 92min
b : 7.67e3 m/s
c : 5.77e10 J
d : -1.18e11 J
e : -6.0e10 J
f : 6.64e6 m
g : new period ~89min; difference ~150 sec. Since Picard was initially behind by 90s, this means he is now ahead by about a minute or so.

I should double-check my numbers on #68, since I did it a bit quickly ... but I believe they are correct. Update: they are correct after a double check, except g) is closer to a minute.

Problem 9 / HW10

2009-03-26T21:37:00.002-05:00

There is a mistake in the beginning of the hint ... the first expression for velocity v(y) is inverted.

I will fix that and clean it up a bit in the next hour. The proper expression for velocity is

v(y) = (const)*sqrt[y/(R+y)]

where "const" involves G's, M's, and R's. Possibly even a 2.

Keep an eye out here for the revision soon.

Constraints vs. real forces

2009-03-26T01:49:00.005-05:00

It is confusing sometimes to realize what is a real, live force, and what is not. For instance, circular motion. You draw a free-body diagram, and sum up the forces. This is one side of the equation. The other side is your constraint on the motion, namely, that for a circular path a net force of mv^2/r is required. Sometimes, we call this "centripetal force," and that is highly misleading. It is not a real force, but a fictitious force, which basically means that if you impose the requirement that the motion is circular, an specific constraint is placed on your force balance.

When you think about it, your force balance always has a constraint, namely, that the net force has to result in mass times the acceleration required to produce the observed path. For a straight line path, zero acceleration, the force balance is zero: equilibrium. For a circular path, the required acceleration is v^2/r, so if circular motion is observed then the net force divided by mass must give v^2/r - if not, then you don't have circular motion. For generic paths, it is more complex: an observed path constrains the force balance, but it depends on the speed along the path and the local radius of curvature.

The confusion is, in my opinion, largely an unfortunate artifact of history and terminology. There is no centripetal force, it is just a boundary condition on your force balance that enforces circular motion.

Anyway: here's what I wrote to one of you earlier. We'll touch on this again in class tomorrow.

In the middle of page 336, in Equation 13-12 (F_n - m*a_g = m(-(omega^2)R)), why do we have a negative sign on the right side. I feel like gravitational acceleration (weight) and centripetal acceleration, both being directed toward the center of the earth, should have the same sign. Here, if you put them on the same side, they have opposite signs.

It is a little bit confusing because the centripetal force is not a true force in its own right, but only the *result* of all other forces. The language in the text is confusing in this regard.

What it is saying is that there are two real forces acting: the normal force acting upward, and the gravitational force acting inward. Since the box follows circular motion by virtue of being on the earth's (rotating) surface, we know that the *constraint* on the force balance in magnitude is that it must sum to mv^2/r. The constraint on direction is that it must be directed radially inward to result in a circular path.

Saying that "centripetal force points toward ..." or "the centripetal acceleration points ..." is misleading. The left side of the force balance contains all the real forces; the right side contains the constraints on the motion from the known path:

(1) straight line: constraint is that forces sum to zero
(2) circle: constraint is that forces give mv^2/r to be consistent with the path, pointing radially inward.
(3) general: what we derived a while back; sum of forces relates to the rate of change of speed and the local radius of curvature of the path.

So it is OK that they have the same sign - it says that the net force balance comes out in favor of gravity, and the net force (which we call the centripetal force, misleadingly) points in the same direction ... we stay on the surface and don't fly off.

Thursday's class (26 Mar09)

2009-03-26T01:30:00.004-05:00

Today, we will focus on applying the general ideas I presented on Tuesday. This will start by motivating the full form of Newton's general law of gravitation, and the principle of superposition. This will allow us to handle the gravitational force between arbitrary (non-point-like) objects like spheres and disks and so forth, as well as the gravitational force above the earth's surface. You should have read most of Ch. 13 by now ...

As a side bonus, we'll figure out what really happens if you drill a hole through the earth.

This will lead us to gravitational potential energy, which will reduce to mgh close to the earth's surface, and lead us to the energy required to achieve stable orbits around a planet/star/etc. From there, we already derived Kepler's laws, and that is that.

I hope to spend a good amount of time on the homework problems for this week and some other examples, at the expense of what is normally reserved for lab time. In what time is left, I want to see your progress on rocket calculations and what your next plans are.

Friday, I will announce another small rocket-related project ... next week, each team will have to present a short progress report.

Problem set 10, number 9

2009-03-25T01:11:00.002-05:00

Having worked it out myself last night, I realized that problem 9 is a bit more ... punishing than it really ought to be. The physics is easy, but the integral you need to solve is somewhat pathalogical.

Thus, the MASSIVE HINT, which sets up the integral for you and gives you the basic result. Note that I said "Use any means necessary to evaluate the integral required." This means you can look it up, perhaps with the Wolfram Integrator.

If you read the hint carefully, there are bonus points for solving the thing the hard way, and further bonus points for proving that it reduces to our usual expression for small heights.

Further hint: don't reinvent the wheel. What are the odds I made this problem up, and what are the odds that it comes from any number of advanced mechanics books?

Turning your homework in late ...

2009-03-25T00:10:00.002-05:00

If I haven't started grading it yet, it isn't late. If the solutions are not posted yet, the grade reduction is likely to be minimal.

This is something of a gamble ... but always turn it in. It is highly likely that even disgustingly late and incomplete homework will merit some credit, which is better than nothing.

Sigh.

2009-03-24T23:45:00.001-05:00

Snipped from an article on wired.com:

Toyota's bland bar graph makes saving gas about as much fun as a physics lecture.

Sigh. Having attended my fair share of physics lectures, they do make a good point ... you can only aspire to be an occasional exception to the rule.

One more hint

2009-03-24T20:08:00.001-05:00

11.13

On 11.13, we managed to find alpha, but we can't find how long the ball slides because we don't know omega at that point. We know we can solve for the rest of the problem, but we're stumped right here.

Ah, but you do know omega at the point that slipping stops - at that point, it is pure rolling motion, and v = r * (omega). That's what you found in the first part.

You know that the linear velocity starts out at v_i, and ends up at v at the moment t that the sliding stops. That means

v(t) = v_i + at

where a is the acceleration you already found. For the angular part, you know that the ball starts out *without* rotation, so (omega)_i = 0. At the moment rolling without slipping starts, you know (omega) = (omega)_i + (alpha)t = (alpha)t. You also know what when rolling without slipping starts, v = r(omega). Put that together ...

v(t) = v_i + at = r(omega) = r*(alpha)*t

Now you know everything but t in the equation above ...

compiled HW hints

2009-03-24T19:18:00.006-05:00

This is stuff that I sent to various people this afternoon ... just so you all get the same info. Forgive the lack of useful typesetting on the math, this is cut & pasted from plain-text emails.

11.13 (#3)

for number 3. i doesn't give us a mass of the ball, so are we supposed to calculate exact values or just symbolic solutions?

in the end, you shouldn't need it ... the mass should cancel everywhere.

for instance, on part b, you want the acceleration. the only force is friction, f = (mu)mg. acceleration is f/m, or (mu)g.

for part c, you want angular acceleration, which is (torque)/(moment of inertia). The force is the same f as above, acting at a distance r. the mass occurring in the torque will cancel with the factor occurring in the moment of inertia.

the other parts are similar - you only need velocities and so on, and since the accelerations are independent of mass, so are they. Let me know if you get stuck on a specific part. The answers of this one are in the back of the book too.

10.67 (#2)

We've pretty much figured out that our tangential acceleration is not
constant, which is pretty obvious since we're told to find it at 35
degrees, but we have no idea how to derive it. We managed to solve for
omega, but that really only gave us a single number, and there's not
really another way to solve for alpha, and therefore tangential
acceleration, since it isn't constant.

you are on the right track ....

the radial acceleration is just a_r = l (omega)^2, since the radial distance is l. That's half of it.

You can differentiate omega, but you want to use the chain rule when you get to the thetas - theta *is* a function of time.

actually, its easier to differentiate (omega)^2 implicitly and avoid the square root:

d(omega^2)/dt = 2*omega*(d omega/dt) = 2 * omega * alpha

Now if you know (omega)^2 = 3g(1-cos(theta))/l, then you also know

d(omega^2)/dt = (3g/l) * d(-cos(theta))/dt = (3g/l)*(sin(theta))*(d theta/dt) = (3g/l)*sin(theta)*omega

Here you have to use the chain rule when you differentiate sin(theta) with respect to time:

d(sin(theta))/dt = [d(sin(theta))/d theta] * [d theta/dt]

Thus, 2*omega*alpha = (3g/l)*sin(theta)*omega. This gives you alpha, which relates to the tangential acceleration via a_t = r*alpha = l * alpha.

Alternatively, you can find alpha by using torque (even though the problem tells you not to, bah!) ... the total torque is moment of inertia times alpha.

10.54 (#1)

For 10.54, is part (b) talking about directions in terms of x- and y-
coordinates or in terms of clockwise/counterclockwise? I'm a little
confused about that because the forces are represented as vectors in the figure.

Just clockwise or counter-clockwise is enough. It wants the direction of the angular acceleration for (b). The angular acceleration is an axial vector, so it has a direction, but also specifies the direction of rotation about an axis. You can specify either one and that is enough, but it is just simpler I think to say clockwise or counter-clockwise ...

So basically, write down which way should it rotate, that's enough.

Tonight's even-numbered question

2009-03-24T19:12:00.001-05:00

10.54: 9.72 rad/s^2

The other two problems due tonight are odd-numbered, and therefore have answers in the back of the book.

Special lecture TONIGHT

2009-03-24T14:01:00.001-05:00

Something I forgot to mention in class today that I just found out about:

At 7pm tonight Dr. Nathan Smith, UAB School of Medicine's assistant dean for admissions (and professor of Psychology) will be speaking at the AED meeting in 30 ten Hoor.

If you are interested in medicine, and contemplating medical school, this is a great chance to hear from someone who actually evaluates medical school applications for a living ...

More action photos

2009-03-24T03:30:00.000-05:00

Rocket launchers in action.

Coding for fun and profit

2009-03-24T03:15:00.005-05:00

By the way: if you enjoy coding, I can probably find you an independent study in the department doing it for a real, live research project. Seriously - there are really not many students around who 1) enjoy coding, and 2) are any good at it. If you can answer yes to even one of those criteria, there is a job for you ...

In particular, the astronomers are always looking for someone, as are the condensed-matter theorists. The particle physicists also do a serious amount of numerical work, and could probably use your skills.

If you think you would be interested, let me know. You have the possibility of getting 400-level physics or astronomy credit during the semester, and actual cash during the summer. There is also no reason why it couldn't be a CBH project, that is not hard to arrange.

N.B. - Fortran is still in common use in physics, as are things like C/C++, python, etc.

Tuesday's class / Gravitation

2009-03-24T01:05:00.005-05:00

For better or worse, there will be much mathness tomorrow. Two things that can help either before or after the fact:

Skim Ch. 13 of your text (gravitation)
Remind yourself about motion on generic curved paths.

The idea is that we're going to "derive" Kepler's laws of planetary motion and Newton's law of universal gravitation from some basic principles and one astronomical observation (viz., the existence of orbits described by conic sections).

In the end, you will not be responsible for the derivations, only the main results. You will see the derivations again in PH301 or PH302 (and possibly MA227). The hope is to show you that the main points of Ch. 13 can be derived with a bit more work, which will ideally help you appreciate them a bit better. Also, all that scary math at the beginning of the semester will pay off again, which is nice.

Once that is out of the way, we'll work on some of the homework problems. Thursday, we will make use of our shiny new results, and be able to show that the remainder of Ch. 13 is a bunch of special cases.

Anyway: tomorrow will be a lot of 'I derive stuff not in the book and you watch' than usual, but not without good reason.

HW 9 solutions

2009-03-23T00:01:00.000-05:00

Here you go.

HW 10

2009-03-22T02:05:00.002-05:00

Yes, the spring break is over. Sigh.

Homework 10 is out, first problems are due Tuesday following the break. The first problems are more angular momentum and torque, after that you will need to read Ch. 13 in your text.

Final exam

2009-03-22T00:56:00.003-05:00

Wouldn't this be fun?

Kidding. Good practice though, they are not all easy questions ... some of them do require Physics II stuff you haven't seen yet. Note 80% is considered a 'pass' by the Diesel Technician Society.

By the way: Moodle is now up to date, I spent quite a while grading over the break catching up. One thing I have noticed: the rate of missed (or partially missed) homework seems to be increasing ever so slightly lately. This is not shocking, being near the end of the term and all ... but be careful. It is not a large percentage of your grade, but the practice is crucial.

Finally: next week is the last week of advising. I am the undergraduate adviser for physics and astronomy. If you want/need to take more physics and astronomy courses, I'd be happy to talk with you about your options and give some friendly advice (that is, in addition to your regularly-scheduled advising sessions if you are not a physics major).

Homework 9

2009-03-11T18:48:00.002-05:00

If you are stuck so far ... don't fret too much yet. Tomorrow we will spend most of the first hour of class on problem solving, specifically setting up the homework problems.

What we did Tuesday was very general and high level, what we missed was putting it all into practice ... and the homework problems are not easy ones. I think by the end of class tomorrow you'll be able to burn through the homework problems pretty quickly.

Photos

2009-03-11T00:16:00.003-05:00

Here are a few cell-phone-camera photos of you sciencing today ...

(If for any reason you object to having your photo online, let me know and I will remove it.)

(Probably should have warned you that I was taking photos ... and I should bring a real camera next time.)

Homework 8 solutions / Tues class

2009-03-10T02:13:00.003-05:00

Here you go.

They are a bit more terse than I would like, in the interest of getting them out quickly (and as a result of it being late). Hopefully they are still somewhat readable ...

For Today' class, we'll begin to discuss angular momentum and torque, which we will finish up on Thursday. Please read/skim Ch. 11 before class if you haven't done so already. We will devote about an hour to the rocket launcher project.

Homework 9

2009-03-09T23:41:00.002-05:00

All problems are due by the end of Friday (meaning, realistically, before you leave for break). With one exception, they are not too bad. Here you go.

In the end there 6 questions on angular momentum and torque, and one odd math problem that somehow found its way to your problem set. You will need to know what a geometric series is ...

The even-numbered H&R problems have the following numerical results, for reference:

11.14: 1.34 m/s
11.16: 0.25
11.66: 32 degrees (this is the bastard problem, FWIW)

Homework this week

2009-03-09T14:53:00.002-05:00

For the record: there are no homework problems due tomorrow. There will be problems due on Thursday, which will come out this evening.

Physics Advising

2009-03-09T13:01:00.002-05:00

This week begins the advising season for the F09 semester, which will continue through the week following spring break. If you are a physics major, thinking about a physics major, or plan on taking more physics in the near future, I would like to meet with you.

Individual meetings only take 15-30 minutes, please let me know if you are interested, and when you would have some time either this week or the week following spring break.

One new thing I should mention is our new seminar course, PH111. It is a 1-credit seminar course with no prerequisites, meeting once per week, and it is devoted entirely to discussing neat topics in physics at a completely introductory level. In the fall, it will meet on Mondays from 4-5:30. Anyone interested in physics is encouraged to take the course, it should be a lot of fun. A tentative syllabus can be found here.

Finally, I would like to point out that all physics majors are eligible for E. Scott Barr scholarships, and we could use some more applicants ... it is not too late to be considered for a fall scholarship! Details here.

Project memos

2009-03-06T17:08:00.002-06:00

By the way: you can submit your project memos in whatever electronic format is convenient. PDF, Word, Pages, Tex, etc., or something more exotic. The odds are very good I can read it.

Trajectory calculations

2009-03-06T14:02:00.002-06:00

Here's a quick snippet of C code that illustrates the algorithm I was talking about today. Some key bits are missing, but it should give you an idea of what to do.

You start with the initial velocity and parameters, and from that calculate everything a time increment dt later. Repeat for many (many) such dt ...

If you don't read C, I can translate it to some other language upon request. If you request something odd like postscript or the like it may take longer ...

Note also that this only calculates the trajectory given some initial inputs. What you want is the launch angle that gives a certain range ... calculating the trajectory is only a portion of that problem.

while (y>=0) {
v = pow((vx*vx)+(vy*vy),0.5);
theta = atan(vy/vx);
ax = ... ; // get these from your force equation
ay = ... ;
vx = vx + ax*dt;
vy = vy + ay*dt;
x = x + vx*dt+0.5*ax*dt*dt;
y = y + vy*dt+0.5*ay*dt*dt;
if (y<0)
y=0; // negative y means we hit the ground
// store various values here
t+=dt;
}

Error propagation

2009-03-06T08:42:00.001-06:00

A nice little post on error propagation, which may be useful for your trajectory calculations ...

Next Friday

2009-03-06T08:22:00.003-06:00

Next Friday - the day before spring break - we will not have a formal recitation. One must be realistic about these things ...

If you are still around, you can optionally show up and we will do some more work on characterizing the rockets and launchers. That is, you can use the time to make some measurements or work on your trajectory calculations and I'll be there to help.

Theory

2009-03-06T06:32:00.004-06:00

This loosely sums up how I feel about theory & calculations. At the end of the day, someone still has to go and look. A reality check, if nothing else.

Also, it is a thin excuse to link to XKCD. Be sure to read the mouse-over text.

Commentary.

More succinctly, and in t-shirt form.