Pendulum "Oops!" to "Opportunity"

It's my first year teaching AP Physics C (Mechanics and Electricity & Magnetism) and I am wrapping up our last Mechanics unit on Simple Harmonic Motion and Universal Gravitation. I had my students work through a simple simple pendulum lab to investigate whether the initial position, length or mass affected the period. I also wanted them to investigate physical pendulum lab and started to research them. Most labs I found used meter sticks with holes drilled in them. While I love using my industrial drill press I did not like the idea of damaging meter sticks I just got with a grant. I found 8-10" pieces of steel bar in my cabinets with two holes in each but that number of holes limited the data my students could take. I realized that hardware stores sell lengths of steel or aluminum bar with pre-punched holes so decided to investigate that.

I was able to find  1/16" thick pre-punched steel bar that was cheap. As  I tried to gather enough pieces for eight lab groups I found several bars that were bent. Remembering the destructive force that is off task high school students I worried that these bars weren't strong enough to last. There was 1" square pre-punched steel tube that was much sturdier so I set up an experiment right there in the aisle. Luckily the nuts and bolts are in the aisle so I found the right size 4" bolt (5/16") and nuts to match. After several iterations (and much waving off of employees) I found that a washer and nut on either side of the tube let the long bolt work as a pretty good axle and held the tube in place. The tubes were more expensive but hardy and I could get two 18" pieces from each one. I also bought a thinner solid bar I would drill just a few holes in for a larger all class demo.

I felt pretty pleased with myself on my way home. Students would be able to adjust the distance from the center of mass of their physical pendulum to the pivot point and conduct multiple trials. The tubes were strong, I have a mounting system that wouldn't let them slide off and fall so I was feeling pretty good.

Then I realized why everyone used bars and meter sticks: they had negligible thickness compared to the length. After asking some other physics teachers it was decided that the effect was probably small:


"For a "flat" piece, thickness along the dimension in the same direction as the axis of rotation won't matter. The "other thickness" will, the moment of inertia about the center of mass should be 1/12M(l^2 +w^2), where w is the dimension perpendicular to the length and axis of rotation. That's going to be dominated by the length term in this case. If you rotate about the end, then you need to add in a (Ml^2)/4 term from the parallel-axis theorem. Since these are rectangular cross sections rather than "flat," the analysis should be more complicated, but hey, we're ignoring all of the holes in the metal, so I'm not sure how far down the rabbit hole we want to go in the first place.

-David Marasco, Foothill College"


Whew! Crisis averted! I sawed the 3' pieces in half (use a fine-toothed blade on a saws-all and a friend), filed the edges and put a bolt on each one. It felt like an easy lab set-up, I could hand one to each group and confidently ask them to vary the distance and find the rotational inertia of the physical pendulum using the slope of a graph.


Fast forward a week and some students let me know that they would be absent for this lab so I needed to make an alternate. I decided to collect stock data, that I would tweak a bit before giving it to them to analyze. When I started plotting the periods I measured for different distances from the center of mass of the pendulum I started to panic. I wasn't getting a line they could take the slope of! Then I called myself an idiot.


Using the equation for the period of a physical pendulum, one gets the impression that the rotational inertia, I, is a constant you can solve for using the slope. But I had forgotten that the rotational inertia would change as the pivot position changed due to the Parallel Axle Theorem:






I thought my students might make the same initial mistake and decided to go with it. For the alternate version students were given hypothetical period and distance measurements for a bar physical pendulum. They were asked to graph it and describe why it wasn't the linear graph they were expecting. Then they would use one position to calculate the rotational inertia of the bar and compare that to the theoretical one using the equation.


I liked the way they would go into the experiment expecting one thing, realize their mistake and still do a few calculations. So I applied it to my whole class activity as well. Timing meant that students wouldn't be able to collect a lot of data and I thought combining group data would help add to their initial confusion. (Because sometimes I'm mean challenging like that.) I explained to students that they had a physical pendulum with holes that they could mount it from and we discussed why they couldn't use the hole (almost) at the center of mass of the tube. Each group was to collect 3-4 data points of their choice and then submit their data to me. We put all data points into a spreadsheet I had made ahead of time. It was nice having multiple groups time the same pivot position to help flush out the shape. Students were concerned immediately about patterns in their data and as the graph filled in more data points in real time there was a furrowed brow on all.


Then, there was the spark, a little "Oh! Wait it shouldn't be straight!" would erupt from some student and they would start to realize their mistake. I showed them this graph I found that matched their own data and they felt relieved. They hadn't broken physics. The rotational inertia changed every time they moved the pivot.

I asked students to choose any one data point from their trials to calculate the rotational inertia at that location. Then we surveyed the groups and found the highest values were at the pivots closest to the end of the tube and the smallest were closest to the center of mass. Students recognized that trend form our initial work with rotational inertia; moving the pivot farther and farther from the center of mass makes it harder and harder to rotate as quantified by an increase in the rotational inertia.

I asked students if there was a way to get the rotational inertia of the pendulum as if it was pivoting at the center of mass and after some discussion they realized that they could subtract the Parallel Axis Theorem value from each of their values. They ended up getting fairly close answers despite different groups taking the data and choosing different pivot points. Win!

With the unintended complexity of the tube vs the bar I'm quite pleased how it turned out. Students were able to confirm facts they knew and learn some new ones while getting hands on. And now they know some fundamentals about physical pendulums way better than reading about it.

How to cheat on your next eye test

Next time your at the Department of Motor Vehicles renewing your driver's license, don't be surprised if you see people in the lobby staring into spinning spirals just before they take their eye test.

Why? It turns out an old favorite illusion, referred to as the "expanding motion effect," can induce increased visual acuity. This illusion is demonstrated in the Exploratorium's "Depth Spinner" Science Snack. It's a perennial favorite among visitors to our ExploratoRio Open House event.

In any case, researchers at the Universities of Glasgow and York incorporated use of the illusion with eye chart tests.

The team discovered that visual acuity—the ability to see fine detail—can be enhanced by an illusion known as the ‘expanding motion aftereffect’. While under its spell, viewers can read letters that are too small for them to read normally.

When participants stare at the center of a spinning pattern that spirals inward for about 30 seconds, shifting their view to a stationary object will induce the illusion that the static object is expanding.

Participants who started with normal visual acuity and saw [inward spinning] spirals ... showed improved visual acuity.

It's as it they were looking through a camera and zooming in on the smallest letters in the eye chart.

It is important that the spiral is spinning inward. Staring at an outward spinning spiral induces a shrinking effect.

Those who saw [outward spinning] spirals ... actually performed worse after exposure to the spirals.

Anyone who's enjoyed this illusion knows the effect is temporary.

But don’t throw out your eyeglasses just yet: the researchers note that the overall boost to visual acuity is small and fleeting.

I would not have expected this outcome. Hat tip to Richard Wiseman's appearance on Skeptics' Guide to the Universe. The Sun ran an article with the obligatory animated spinner.

Kids these days

When I was a new teacher, I was wary of veteran teachers who complained about "kids these days". The gist was that students of a long ago yesteryear were capable of hunkering down and rising to the challenge of rigorous academic coursework, while today's students simply cannot hack it. I didn't see it. My students were rising to the challenges I set before them. What was the problem? I never wanted to age into that seemingly inevitable "get off my lawn" stage.

Back then, a veteran teacher was anyone with ten or more years in the profession. But it was those with more than twenty years in the classroom who were most likely to shake a "kids these days" fist.

I now have more than thirty years of classroom teaching under my belt. And I now see why it happens. The struggle is real. And I don't have a ready solution.

In my own recollection, my Physics students of 1996-97 figured it out better than those of any year I've taught. (I'm referring to my Physics students in this post, not my AP1, AP2, APB, or CP students.) 

In 1996-97, I was entering my second decade of teaching and had settled on some pedagogy and policies that seemed to work for me and my students. A large majority of students in 1996-97 (N=116) essentially agreed to my terms and prospered as a result.

In contrast, my Physics students in 2018 (N=60) have largely opted out of my conditions and suffered predictably. Here's a side-side comparison of the grade distributions.

There were four sections of Physics in 1996-97; there are two sections in 2017-18. (There was one section of AP Physics B in 1996-97; there is one section each of AP Physics 1, AP Physics 2, and Conceptual Physics in 2017-18. These classes are not included in this analysis.) Seventy percent of Physics students earned an A or B in 1997; only 57% did so in 2018.

Why the dramatic difference? In my analysis, it is engagement. Engagement is difficult to quantify for purposes of comparison. My best method for quantifying engagement in 1997 relates to random homework checks. 

By that metric and its built-in tolerances, 29% of Physics students were very engaged in 1997, 45% were somewhat engaged, and 26% were disengaged. 

Since 2014, we have had a Test Correction Journal (TCJ) process by which students can earn back up to half the points they missed on each unit test. "Sweat equity" is required: students spend class time writing "journal" entries for each test item they missed. Completed journals grant students access to a ten-question quiz. A 10/10 gets you half your missed points back; 7/10 gets you 70% of half the points you missed, etc..

So I can now use TCJ performance as a measure of engagement. We have five unit tests in the first semester. Students who participated in all five are rated as "very engaged". Students who participated in four of the five are "somewhat engaged". Students who missed more than two TCJs are "disengaged". 

By that metric and its built-in tolerances, 28% of Physics students were very engaged in 2018, 27% were somewhat engaged, and 45% were disengaged. 

Here is how the Physics grades break down (2014-2018) when classified by levels of engagement. (N=382)

That infographic might take a moment to absorb. The green columns are grades earned by highly engaged students: mostly As, fewer Bs, fewer Cs, two Ds and no Fs. The yellow columns are grades earned by somewhat engaged students: some As, more Bs, some Cs, a few Ds, and two Fs. The red columns are grades earned by disengaged students: one A, more Bs, many Cs, dozens of Ds, and all but two of the Fs.

Excel is happy to make pie charts as well. Here are the grade distributions by engagement level.

Eighty percent of very engaged students earned an A or a B.

Somewhat engaged students were somewhat distributed across letter grades.

Half of disengaged students earned a D or F. One out of 382 earned an A.

My own assessment is that students who engage in the course will get a good grade. There is more to engagement than Test Correction Journals. Homework engagement is crucial. But I have no way to measure that, whatsoever.

Still though, you will most likely earn an A or a B if you are at least engaged in the TCJ process. You will most likely get a C, D, or F if you're disengaged.

Some might argue that in addition to preparing and maintaining quality physics pedagogy and policies, I have an obligation to compel or otherwise force students to engage in the course. I cannot bring myself to agree. 

At some point, students must have the option to engage or not engage. In my own highly biased assessment, I consider my course to be highly engaging as it is. And I believe there is a valuable lesson to be learned about the consequences of choices that we make when approaching an academic course. Physics is a college prep course; many students will be sitting in college courses in less than a year. 

I want my students to succeed. In my class and beyond. I know that no one will chase them down in college to make sure they are duly engaged in their coursework. If they know how to engage on their own, they will be set to succeed to the limits of their abilities.

Full engagement is not a guarantee of an A. An A represents a level of mastery that is demonstrated in various assessment instruments. Engagement puts an A, B, or C in play while virtually precluding a D or an F. Disengagement, on the other hand, operationally precludes a student from earning an A.

Choices and consequences.

Am I at the "kids these days" stage? I don't think so. Engaged students are doing very well in the course. Top grades are well within reach of anyone willing to engage. And AP students (unsurprisingly) remain highly engaged. I am bothered by the increasing number of students who choose to be disengaged in Physics.

One last graphic to convey my disappointment. This is this year's 1st period Physics class's test scores. This was the most disengaged class I've ever had. In the test scores field, red indicates a TCJ that the student missed. Yellow indicates a test that was made up during the make-up period following the administration of the test (usually about 10 school days). Blue represents a test that was missed and not made up in the make-up period. It was made up at the end of the semester. Black is a second test that was missed and not made up in time. It goes down as a zero. The letter grades are shown in the leftmost column. Green shading for very engaged students, yellow for somewhat engaged students, and red for disengaged.

Kids these days? No. Shaking my head? Yes.

"Magnetic"—a song to add to your physics playlist

There comes an awkward moment in my AP Physics 2 course when we arrive at the topic of electromagnetism. Students enrolled in Physics last year studied magnetism in some depth, with a robust qualitative laboratory component. Students enrolled in AP Physics 1 did not hear the term "magnetic" in class at all: there is no magnetism in AP1.

So I segregate my AP2 charges by which course they had las year. The former AP1s move quickly through the Physics course material while the former Physics students get some enrichment by way of The Mechanical Universe, Conceptual Physics Alive, and Nova. Eventually we reunite and move into deeper issues of electromagnetism and induction, ending up at Faraday's Law.

The Nova episode is S31E07, "Magnetic Storm," concerning the changing nature of Earth's magnetic field. [Warning: do not make a drinking game out of each time a thunderbolt sound effect is deployed—you will not make it to the end.]

Nova - Magnetic Storm


In developing a video question set to accompany the episode, I noticed that a pop song was featured heavily throughout the episode. A bit unusual for Nova in my experience. The end credits included the name of the artist but not much else. It was enough to track down the... track.

It's Judith Edelman's "Magnetic" from the 2009 Thirty One Tigers release, Clear Glass Jar, available on iTunes, Amazon, and wherever fine music is sold. Someone commented that Edelman's "Magnetic" is to electromagnetism what Don McLean's "Vincent" was to the art of van Gogh. You be the judge!

Judith Edelman - "Magnetic"


A comment for the video included the lyrics.

It's the buzz when I'm full
Of your sweet magnetic pull
It's the tug that I crave
It's how opposites behave

Is electricity all there is to you and me?

In the fields, in the fields
Where the static is revealed
If the north isn't true
Will I lose my way to you?

Is electricity all there is to you and me?

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

In the deep molten heart
Where these strange attractions start
If we are passionate
Will this rock remember it?

Is electricity all there is to you and me?

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

What's gonna happen when the magnetism fades?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

It's the buzz when I'm full
Of your sweet magnetic pull

Egg Toss video because—why not?

The final batch of clips from Grass Omelette XVII at Rio Americano. A nice catch and two spectacular splashes! With no sun, we were able to line up with the geometry of the field. Seems we should have taken a bit of Sharpie to the eggs to increase their contrast with the sky.

Large impact time to reduce impact force


Impact force too large #1



Impact force too large #2


Previous Grass Omelette XVII coverage can be found here:
Splash and Catch: Grass Omelette XVII

More robust coverage of this activity can be found here:
Egg Toss 2013

Be Direct With Me

I am a huge fan of a CBC podcast called "Under the Influence with Terry O'Reilly". Tales of drunk Canadians engaged in Molson-fueled shenanigans? No. Each half-hour episode tells a carefully woven story connecting some element of advertising or marketing to the world where you live. You will learn things you didn't know about things that you do know with each episode. And each episode is the product of 20-30 hours of research. Subscribe to the podcast right now while you're thinking about it.

In an episode called "When Madison Avenue Met Broadway: The World of Industrial Musicals," O'Reilly played a few seconds of "Be Direct With Me". Just a few-second bite with not much to identify it. But I was transfixed. I deployed my hard-earned blue belt in google-fu and sourced the track. I then saw it was available on iTunes and paid for it immediately (I'm old and from the midwest).

I quickly set the track to a Keynote preso and roughed out a nice delivery. Then I spent several days refining and improving. I simply had to show this gem to my colleagues at the High School Share-a-Thon attached to the American Association of Physics Teachers Winter Meeting 2018 in San Diego.

High School Share-a-Thons can be lively affairs, typically held in the evening on Day 2 of the conference: between the workshops and the invited/contributed talks. For reasons nobody ever explained to me (and I asked), this year's Share-a-Thon was scheduled for 8:30am on Day 2, conflicting with many workshops. And... in the morning!

A few dozen intrepid instructors braved the San Diego rains and made it to the event. Sadly, the session presider did not. A few years ago (I want to say it was the Omaha Summer Meeting), the Share-a-Thon was left without a presider and I stepped up to awkwardly host.

Someone in the room in San Diego remembered that, and promptly ratted me out. So I was once again drafted into service. When the session began, only two of the several dozen attendees signed up to share. We had the room from 8:30am until 10:00am. I made the executive decision to dispense with the five-minute time limit and encouraged my colleagues to not be bashful—we're all friends here!

I showed a couple of things (videos of those things, anyway, as has become the trend among traveling physics sharers). Then I hit them with the video below. I truly didn't want to be up first for this event, but it was what it was.

In any case, the presentation. You will want to be sitting down for this.



I had a few more slides of humor and fun for my live preso; I intend to show it again at the NCNAAPT Spring Meeting.

Eventually more folks came up to share. Questions were asked and answers were given. We ended the session at 9:59:50am.

But industrial musicals? I had no idea. And they were huge in terms of budget, scale, and talent.

UPDATE: GE's Go Fly a Kite—the industrial musical from which this song comes—was written by the composer/lyricist team of Kander and Ebb, who also wrote Cabaret and Chicago. The double-album original soundtrack (souvenir recording) can be had via eBay for $99.99 as of this update. But it has also been posted to YouTube. I found "Be Direct With Me" as the opener for Side 3. The video shows the liner notes and dress rehearsal stills that correlate to the currently-playing track. While Valerie Harper was arguably the biggest enduring star in the cast, she did not sing "Be Direct With Me". Who did? Carole Woodruff. The only other credit I was able to find for her was a musical called Pleasures and Palaces, written by Frank Loesser and choreographed by Bob Fosse. It ran for a month in Detroit and was not reviewed kindly. Woodruff is the last singer listed in the credits. I have found no other relevant information on her.

You spin me right round, baby, right round ...

Well, my accelerometer anyway.

I'm in the middle of my first year teaching AP Physics C and we ended last semester with rotation. Therefore, I'm looking at any spinning or round thing in a different light. I was at the RAFT San Jose store and saw giant wooden circles with rough edges for cheap. And this is RAFT cheap so I think it was <$4 for 8 of them. I snagged them unsure of what I would do with them and took them home to be inspired.

I ended up sanding down the rough edges to find they were very sturdy and furniture grade plywood. Since they were leftover from some manufacturing process they were perfect circles. I decided to make them into giant tops/ turn tables. I envisioned students playing with them at the onset of this unit to observe changes in rotational quantities, maybe use some slow mo video or accelerometers. Or perhaps we could use them for conservation of angular momentum. The possibilities are endless!

I reviewed some geometry and found how to find the center of the circle. I measured equivalent length chords around the circle and marked halfway across each chord. From this halfway point I drew a line perpendicular to the chord towards the center of the circle. Doing this a few times gave me a point, or at least a small area of the "center" of the circle. Since I was drilling a big hole in the middle I figured close was going to be ok.

We have a drill press in our mini-shop in the Physics prep room. I used a 7/8" drill bit to drill a hole in each disk. This allowed me to fit a 1/2" PVC pipe through the hole with a bit of wiggle room. Going down to a 1/2" bit was too small of a hole for the PVC to fit so the hole had to be a bit bigger. But "wiggle room" meant that if I turned the PVC axle the disk wouldn't rotate at the same speed. Hmm...

I used smooth 1/2" PVC endcaps on the bottom of about a foot of 1/2" PVC for my axle. The endcaps had the manufacturers logo on it so they did not have a perfectly smooth bottom. If it bothers me enough I may go back and file them smooth. I found that wrapping the PVC with a bit of masking tape increased the diameter of the pipe enough to fit in the hole in the disk snugly. Through trial and error I found about 3 times around worked well. Too tight and I was banging the axle against the ground hoping the disk's inertia would drive it down onto the tape, sometimes that worked. I put a second end cap on the other end of the axle for comfort.

In the end I had 8 tops for use. By the time I made them it was towards the end of the rotation unit but they were still helpful. When students were reviewing torque, angular momentum, etc. I left them out with their review sheets. Students would grab them to rotate and discuss vector directions with their partners.

I also played with the Physics Toolbox app's accelerometer by placing it on one of them and giving it a few turns. Next year I'd like students to investigate the acceleration recorded by the phone at different radii as they turn it with the same speed. Below is a quick video of the attempt.

I had considered sharpening down dowels to a point as the axles instead. But, I teach high school and a sharpened dowel through the center of this disk might become a spear with a shield so ... no.