Teeeeter Totr

Just a quick balanced torque puzzle. It's really a test of whether or not one truly accepts the concept of center of mass.

Nothing exotic going on. The meterstick is uniform. Sufficient information is provided to solve the puzzle. It can be confounding to students.

Teeeeter Totr - HTML export | movie export

UPDATE: Among the many things I can count on in life is that virtually any mechanics demo I might share here has already been done better by the inimitable Dan Burns. For example:

Torque-Master Challenge 2019

After completing the "Torque Feeler" / "It's All in the Wrist" Conceptual Physics Lab Manual activity, we add the Torque-Master Challenge.

We again repurpose our five-foot aluminum tube from the Pasco Scientific Lenz's Law Demonstration set. Sometimes we use it as a blow gun. Sometimes we use it for examples of resonance. This time, we tie an ordinary 500-mL water bottle to the end. Challengers must hold the arrangement level for ten seconds.

Over the years, I have found that very few of my students can do this. I can, and I am not young, cut, ripped, or chiseled. And I do not lift. I mean, look at me in the video. Honestly!

Torque-Master Challenge 2019


Why I can do this while so few of my students can is a mystery I have no answer to. Now that I think of it, though, very few of them can match my speed when we use this tube as a blow gun. I have no explanation.

When we find students cannot match my blow gun speed, I admonish all of them to quit smoking!

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.

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.

Can you feel the inertia?

I just started rotation in my AP Physics C class and I introduced moment of inertia today. There was the traditional hoop vs disk down a ramp and I found an inertia stick for students to observe. The first class went very poorly because I introduced the rolling inertia demonstrations before we had talked about rotational kinetic energy and rolling ... BUT I did develop a new demo that did work so let's focus on that.

My textbook has a lot of pictures like this one of unusually shaped objects:

The odd objects are meant to illustrate that the moment of inertia is different with different axis positions. This concept will also help explain the Parallel Axis Theorem if the object is not one of the uniform shapes commonly seen on a moment of inertia chart. I wanted to make something like this with a movable axis so that my students can feel the difference in inertia at different axis points. Its a good thing I have a mini-shop in my prep room ...

I found a scrap piece of 3/4" plywood and used a bandsaw to cut it into an "odd shape." Then I drilled three 1/2" holes through it, one on each end and one roughly at the center of mass. I cut three 8" pieces of 1/2" dowel, one for each hole. The dowel was snug enough that when you rotate it, the whole piece rotates.

The wood is hefty enough that you really feel a difference from the center axis to one on the end. You can feel a slight difference between the two ends but not as much as I'd like. I may carve out a bit more so that the difference is easier to feel. Below is a video of me spinning it to give you a sense of it. 

Trick or treat? See for yourself

It's been a little quiet around here for a variety of reasons. So let's shake off some dust for ... Halloween? Why not?

Four drops of food coloring are added to the center of a half-filled "skinny fish tank" (a.k.a., Arbor Scientific Laser Viewing Tank) resting on a low-friction turntable (Pasco's Rotating Chair platform).

The tank is then given a spin. And, well..?

It made me say those magic words all people in science prize: "That's funny!" I didn't know what to expect, so in some ways, this wasn't overwhelmingly surprising. Still though...



I get the parabolic surface. But what's going on in the dye? I'm sure there's a lovely, simple explanation that I should know. But I don't.

If you do, kindly leave it in a comment. I am your student.

Reliant Robin Revisited

To accommodate a school-day administration of the PSAT this Wednesday, classes will meet for 20 minutes. What can you do in 20 minutes? Last year, I developed a mini-lesson around Top Gear's segment on the Reliant Robin.

I added a few questions to that lesson this year. I feel best when there are a nice, round 10 questions.

Access the video here (I recommend downloading videos for classroom use):
Top Gear's Reliant Robin

Oh, and I did figure out how to post the video here for additional convenience. Isn't it nice to learn?

Updated question set and answer key:
Rolling through Roundabouts in a Reliant Robin @ TPT

What do you do with a 20-minute class session? Let me know in the comments.

Torque Sticks

During our unit on torque and center of mass students hang meter sticks from ring stands to find their center of mass. But these meter sticks have one end wrapped in lead solder so that the center of mass is not at 50 cm. Students hang the meter stick from a fulcrum they could shift and added weights to the other side of the meter stick until it was level. They complete at least three trials to determine the unseen center of mass.

 While this moves the center of mass considerably I have two problems with it:
1. I was a little concerned about exposed lead solder so I wrapped each hunk with electrical tape. Once I put the solder piece on students were not to move it. Sometimes students listen, sometimes they don't.
2. Students did not think about the lead solder as part of the meter stick, as if it had a heterogeneous mass distribution. They thought of the mass as an added weight and when drawing force vector diagrams might label an applied force at that point. Or students would draw the Force of Gravity of the entire meter stick as coming from this point, not from the center of mass.

I bought sticks that were very similar to meter sticks but not quite the right height. I planed them down a bit so that they fit the meter stick holders I have. Then I drilled lots of holes into them.

I tested one stick and found that drilling holes on one side only shifted the center of mass about half an inch. I needed to add more mass to one side or remove more mass from the other. I decided to add melted lead solder into each hole. I put tape behind the holes on one side of the stick and then used a soldering gun and iron to melt the 50-50 lead solder into each hole.

 

One of the trickiest parts was trying to keep the puddles of solder below the top of the hole. Its not a big deal if it bulges over but the next tape step is easier if its level. 

I had one stick that was my sample stick, for instance now I know not to try a spade bit as it will crack the wood. On this sample stick six or so lead filled holes on one side of the stick shifted the center of mass considerably. In the bottom right you can see the original center of mass point with empty holes marked beneath the pen and the new location of the center of mass once they were filled with lead shifted to the left a few inches.

So I had a lot of holes to fill with lead. It took almost two hours to fill 184 holes on these sticks.  Every stick has holes on one side (left picture), some of them also had empty holes on the other side (right picture). The majority of the weight shift is due to the lead but taking a bit of wood out of the other side helps a bit. Each stick has a different amount of holes so that the center of mass will be different.

The lead filled hole side got another piece of masking tape covering the lead. This helps with the illusion that the stick is homogeneous even when its not. And it will help protect students from the lead. I looked up the hazards of lead solder and the main issue seems to be ingesting lead dust from your hands after working with it. Washing your hands after working with it seems to make it perfectly safe. 

I plan on using these sticks as part of a lab practical. Students will have to balance the sticks with a set fulcrum position. I can nail the hanger that acts as a fulcrum into one position so that students can't move it. They will conduct a few trials with different masses on the other side (empty/ no hole side) in order to calculate the position of the center of mass. By labeling each stick and keeping a key I will be able to check my student's work. I'm hoping these new sticks will prevent some of the misconceptions involved with this lab.

Dizzying dance demonstrates dynamics

Rotational dynamics, specifically. But I was going for alliteration in the title.

A different staging of this performance floated into my Facebook feed yesterday, and my jaw dropped. And it's not that I don't get out much. It's that this performance is jaw-dropping. And of course it's a beautiful synthesis of artistry, athleticism, physics, and practice. I don't even understand how a human can do this with functional semi-circular canals. Watch for yourself.

Angelica Bongiovonni - 34th Festival Mondial du Cirque de Demain - Paris


So in a #FirstWorldProblems moment, deciding to post this gem to the blog led me down bit of a rabbit hole. The video was locked into Facebook. I don't yet know how to rip videos from Facebook. YouTube, yes. Facebook, no.

The Facebook video linked to the Dance.com Facebook page. That didn't help. Neither did going to Dance.com, itself. The Facebook video didn't even mention the dancer's name. No surprises there. The comment count was in the thousands. Nevertheless, I began poring over the comments and found the dancer's name in a reply to a comment.

Off to YouTube. The dancer had a channel but the channel did not include this performance; it was sparse and seems to have been abandoned. She's apparently too busy dancing to maintain a YouTube channel.

So a general name search ensued. Adding "Cyr Wheel" didn't help. (Yeah, I didn't know it was called a Cyr Wheel. either. You can actually learn things from search results.) I couldn't find the video I saw on Facebook.

But I found the one posted above: Same routine; different performance. I don't see a simple "in" to an engaging paper and pencil companion lesson. But the video can stand on its own. Whenever I show such a thing in class, I verbally admonish my students that they must be thinking about physics as they watch.

One thing Angelica Bongiovanni did post to her wee YouTube channel was a short blooper reel made in preparation for a different routine.

I love the poster frame that shows up for the embedded video. That's the still you'd hope to capture if you were photographing the performance.

YouTube AP Physics 1 Lesson: Backyard water slide

Whoa! The Blog of Phyz has suddenly gone Stephen King prolific! I love it. Many thanks to Bree Barnett Dreyfuss and Dan Burns.

When the following gem percolated up through my Facebook feed. I was inspired to create a lesson. Take a look at the clip, and we'll proceed from there.

Backyard Water Slide Fail



[Note: as with all things YouTube, the specific video link above may someday go blank. Searching for "Backyard water slide fail" will likely find a working link. And it's always a good idea to download the video for posterity. YouTube discourages this, but underestimates your tenacity. And your Fair Use protection.]

My mind expanded the story: why did our water slide enthusiast overshoot the target pool? Why did they put the pool where they did? An AP Physics 1 exercise (perhaps shop-worn even in these early years of AP1) overcame me. So I hacked away.

When trying to fit a physics lesson to a real-life situation, there's always the question of how best to balance "real-world"-ism and "first-year students can solve it"-ism. I did my best; you might have done it differently. I think my distance estimates are reasonable; I didn't do heavy duty video analysis.

My process does get a wee bit ugly, but that's why it's an AP Physics 1 exercise, not a Conceptual Physics exercise. But you get energy, rotation, and projectiles in the mix, so it's a worthwhile activity. And it involves video of a guy hurting himself: few things appeal so viscerally to the teenage sensibilities.

In any case, here's my expansive spin on the video clip.

YouTube Physics: The Ultimate Backyard Water Slide @ TPT

And if you wish to add even more mechanics problem clichés, you could ask how this would have gone down if repeated on the moon.

Lesson for a 20-minute class

Many of our students took the PSAT today at school. After the testing period, we ran periods 1 through 6 at a little more than 20 minutes each.

So we watched and answered questions about Top Gear's segment on the three-wheeled Reliant Robin.

The video is here: Wimp.com—Top Gear's Reliant Robin. The full segment—shown on the Wimp page—is 14 minutes; shorter edits can be found elsewhere (YouTube, etc.). I couldn't figure out how to embed Wimp's video into streaming here.

The questions are here: Rolling Through Roundabouts in a Reliant Robin @ TPT.

Hewitt-Drew-it! Torque

We drop in on Paul's class as he discusses the concept of torque.

Hewitt-Drew-it! PHYSICS 39.Torque

Entertaining equilibrium

If this guy's not a Libra, I shall renounce my faith in Zodiacal Astrology.



Wait: I have no faith in Zodiacal Astrology. Durn.

But what a lesson in balanced torques! And a nice soundtrack, too. The Hebrew of the video's title translates to "Amazing Performance and Power Balance," according to Google Translate.

Your assignment: make a clever number puzzle (standard physics numerical problem) out of this.

Hat tip: Marion Gribskov (my distinguished Rio Phyz predecessor).

Small water beats big bacony beans!

Here's a fun pic from AP Physics today. We raced a solid can of baked beans (with bacon), c.1990 against a cylindrical bottle of water. A student suggested we try catching the result using the Casio EX-FH100's multiple exposure mode. We caught this at the very end of class. The water beats the beans. But why did it win? Sloshy liquid? Smaller radius? Hmmm...

The small water was placed in front of the big beans before they were released to roll down the hill. The farther they rolled, the greater the water's lead became.

Torque on ice

Gunn High School physics teacher (and President of the NCNAAPT), Claudia Winkler, likes this "Physics at the Olympics"... moment!

Take a look: