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.

Simple demo big gains

I have noticed a big difference in student comprehension when the problems become real to them. Simple visuals can have a big impact on the students "getting it." I can't count the number of times I've tossed a tennis ball around to make a point. Somehow holding the tennis ball at different heights or just tossing it up to catch it again can lead to "Oooh now I see what's happening!" So I have several simple demos that help students visualize their problems, a block or two hanging from the ceiling with spring scales, a stuffed toy in a bucket, etc. 

When we studied springs I found a Pasco spring demo set with five springs all of the same length but different spring constants. The first stage was to hang a 20 g mass from the red spring and see it barely settle above the table. I asked students what would happen if I were to hang a 500 g mass then from the green (which they assumed was identical). They were surprised at its shorter elongation and when I asked why they all said "it has a larger spring constant."

For the next stage I set up two large ring stands with another bar clamped horizontally between them. I dramatically assure students it is level with the springs hanging at their relaxed length. Then I hang a 500 g mass from each and they can see the slight differences in elongation. Then the 500 g masses are switched out for 1 kg and the difference between them becomes more pronounced (left). Applying this to Hooke's Law they could all calculate the spring constant for each spring. But this made it way more interesting than five given forces and elongation lengths to calculate the spring constant from a word problem. 

When my AP Physics C class started center of mass, many could calculate the center of mass with equations but had a hard time visualizing what that actually meant. A common problem involves materials of different densities stuck together, for example a piece of aluminum and a piece of iron. To make a real life version I found a piece of Styrofoam that was the same thickness as a piece of scrap wood. I drilled three holes in the wood, stuck three dowels into the holes and stuck the dowels into the Styrofoam. I wrapped the whole thing in paper to make it appear uniform but I did tell students it was made of two different materials. I showed it to students and asked what information they would need to solve for the center of mass. Of course I play with them a bit and after each response I say, "Ok, now you can solve it right?" to which they predictably respond, "No, we need XYZ too!" Eventually, I give them the dimensions of the whole thing and let them solve for it. The dimensions are listed on the paper below (the "total mass" includes the paper in case they ask).

They are not surprised that the center of mass is closer to the wood side but they are surprised that for this particular arrangement it's actually on the wood. It's a simple practice problem but once they're done I can balance the piece on my hand at (almost) the exact position they predicted, about 5 cm in from the wood side. Students that struggle with this homework problem were successful with this in-class practice problem. 

Another simple one my colleague Jessie Chen shared with me can be done by every student in your class on the cheap. Like less than $1 cheap. Most dollar stores sell packs of cards for $1, or even a double pack if you're lucky. Each student will need one plastic playing card (or index card) folded at a right angle along the length of the card. Place it on the corner of the table with one corner hanging off the edge of the table. Place two pennies on the card so that one is on the portion on the table and one is on the portion hanging off the table. You can use a pen or pencil to press on the card so that when it moves it pivots around that point. Flick the vertical part of the card on the side that is hanging off the table. This causes the card to move so that it is no longer supporting the penny hanging off the table and it will fall straight down due to gravity. On the other side the vertical portion of the card will push forward, applying a horizontal velocity to the penny and making it shoot off the table in a half a parabola shape. You can hear (and see) the two pennies hitting the ground at the same time. Many of us have a fancy machine that demos this for us, sometimes called a "Drop/shot" or a Newton's Second Law machine, and those work great, don't get me wrong. But to be able to hand these to my students and have them try it, nothing can be better than that! 

Lab equipment older than me

While continuing to clean my prep room (no end in sight!) I found more old Macalaster Scientific Corporation boxes similar to the radiacmeter and dosimeter I found a few weeks ago. I found four different pieces of equipment, it has been interesting to research them, find out what they were used for, and try to determine if they can still be used. The company seems to have stopped production in the 1960s, although upon searching for their equipment I see many familiar things. My dynamics carts from my Crash Cushions project are apparently made by Macalaster and potentially 50 years old. Perhaps new dynamics carts will be on my shopping list this year ...

Mass of an Electron Apparatus
This uses a "Magic Eye Tube" with a circular display that was used to tune radios in the 1930s. My equipment, shown below left, had to be used with an air core solenoid, shown below right. From what I can tell these can still be purchased for about $100 each (solenoid not included) and used as demo equipment.

The instructions puzzled me a bit as they referred only to assembly so I turned to the instructions of a similar modern version.

This video shows the magic eye tube changing as a radio is tuned in and out:

It took me awhile to realize that when not used with a radio, the magic eye would produce a straight edged fan shaped wedge that would be unchanged (bottom right).  That is, unless a magnetic field is brought near it to bend the electrons and the fan shape on the display (bottom left).  That is where the air solenoid comes in, constructed to be about twice the height as the fluorescent screen on top of the magic eye tube so that it sits at the center of the solenoid. The magnetic field around the solenoid when current is running through it effects the electrons on the fluorescent screen.

The explanation describes an experiment to determine the mass of an electron approximating the curvature of the "fan" shape using something else round. You seem to need to know multiple voltages, the current and turns in the solenoid (to determine's magnetic field strength) and the curvature of the bend. The instructions end with "Refer to physics text books for the formulae relating to the calculations for the strength of the magnetic field and the velocity of the electrons. From this information you can calculate the approximate mass of a single electron." Not quite spelling it out for us, is it?

I found this image and equations on Hyperphysics that I think match up with this experiment.

I'm not 100% sure that this is the correct equation for finding the mass of an electron with a magic eye tube but it looks promising. The radius of the curve of the electron deflection due to the solenoid's magnetic field would be found by matching it to a circular object. Since it would be hard to accurately measure the radius of only part of a curve, the instructions suggest that if you find something else that has the same curvature but is a complete circle it will be easier to measure the radius. The magnetic field strength of the solenoid could be found by knowing the current through it and the number of coils. The voltage should be measured from the circuit, charge on one electron is known and that should reveal the mass of one electron.  

Potential Difference Kit
From the brief assembly instructions I think (1) I'm missing an insulating handle and (2) it is acting like an electrophorus. (Here is an Electrophrus Engineering activity by the way.) That is my guess at least, maybe someone else has a better idea of what this #unknownequipment is used for.

Tangent Galvonometer Kit
The dismantled frame (left) can be assembled (right) to make a base to hold a compass and a loop of wire. A compass (not found in the box) would be placed where the spool of wire is placed on the right. A square loop of wire is made around the four nails (two top, two bottom) that surround the compass resting on the base. This modern version shows the same set-up. There are fancier equivalents of this kit with secured circles of wire around mounted compasses. I've made similar set-ups for students with cardboard in class (start video about 30 seconds in).
I was surprised to read "This can also be used to determine the magnitude and direction of the horizontal component of the Earth's magnetic field." in the description. I found this explanation of the experiment but I'm not sure if this particular rudimentary kit would be successful. This kit is quite large, about a foot tall, and has sharp aluminum edges. This particular one has been defaced with an engraved swear word as well. While it could be useful, I can probably make some that are a bit easier to worth with.

Cathode Ray Tube
I figured it lit up when I saw it but Dan was able to tell me that this piece of #unknownequipment was a Cathode Ray Tube. This Lab Guy post shows how it could be hooked up and made to work like a small TV. That is way above my current summer level of work load though. Dan also said he powers one with a handheld Tesla Coil so until I procure one of those this may not be useful.

While I might be able to get some of these to work, some would require purchase of additional materials. One could find such vintage pieces on eBay but it begs the question, do you want to? They still hold some educational value, if their original purposes are known, but it may not be worth trying to get them to work. For the time being they will remain on a shelf with other vintage pieces I can't bear to part with.

How many magnetic poles?

Last weekend I presented at the Exploratorium's 4th Annual NGSS STEM Conference "Making Science Count: Integrating Math into an NGSS Classroom." I presented a few inverse and inverse square relationships participants explored using hands on experiments. One of them was to investigate the relationship between the strength of a magnetic field and the distance to the object.

Thanks to sponsors, participants were able to go home with their own "cow magnet" (if you don't know why they are called that read about Hardware Disease). While preparing for the workshop that morning senior scientist and staff physicist Paul Doherty cautioned me that while I would expect cow magnets to be dipoles they could be tripoles. After he check with magnetic viewing film it turned out they were quadpoles. And that can complicate an experiment.

Workshop participants either borrowed my Vernier Magnetic Field Sensor or used the magnetometer on the Physics Toolbox app during the workshop. When I was preparing for the workshop I found that this could be an inverse square or an inverse cubed relationship depending on the physical dimensions of the magnet. Given the orientation of these quadpole magnets if you rotated the cow magnet at all as it approached the sensor the polarity could change.
1. Asking questions (for science) and defining problems (for engineering)
Below is a video using a dipole donut magnet, a dipole cow magnet and a quadpole cow magnet that models what I would expect students to see.

I investigated further using my Vernier Magnetic Field Sensor once I got back to school. Below is a graph made by starting the sensor perpendicular to one end of the cow magnet and then moving up the length of the cow magnet to the other end. I put a pencil in between the cow magnet and the sensor to maintain the same distance between them.

On the left, the red line was made using a dipole cow magnet and the blue by the quadpole magnet. In this case they are similar and one might conclude that they are both dipoles. (Differences in slope are due to the sensor's speed.) On the right, the red line is the same, made with the dipole magnet. The orange and green were both made with the quadpole magnet. When the green line was made the magnet must not have had a pole directly facing the magnetic field sensor.

I also pointed the sensor at the end of the cow magnet and rolled it along the table, keeping the sensor from rolling and at the same distance away. I tried it twice with the quadpole magnet, creating the green and purple lines in the middle. This was harder to keep steady but you can see the polarity switch as the lines pass the time axis. Repeating the experiment with the dipole created the brown line at the top of the graph. For the dipole rolling it made no difference in the polarity strength or direction. 

So what can you do with a pesky quadpole cow magnet? Why, confuse your students of course! I plan to hand groups of students one dipole and one quadpole cow magnet and ask them to determine the number of poles on each. If they are lucky they will get a compass and/ or viewing film. Otherwise having two magnets should be interesting enough. If you're keeping track of the NGSS Science & Engineering Practices, such an investigation could lead to quite a few of them in one lesson:

2. Developing and using models [of thinking]
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations (for science) and designing solutions (for engineering)
7. Engaging in argument from evidence
8. Obtaining, evaluating, and communicating information

Make your own Transit Light Curves

I highly recommend the educational activities from SETI; especially their Kepler Mission materials found here. There are NGSS aligned activities arranged by age level. I'm looking into the Transit Tracks activities to link Kepler's equations with the Kepler mission, light and our Universal Gravitation unit.

Within that document SETI describes a demo of the Kepler mission by passing a bead on a string in front of a light bulb in a dark room. There is a note off to the side that says:

Optional: Collect Real Data
If you have a light sensor, computer with sensor interface, graphing software, and a computer display projector, place the light sensor in the plane of the planet/ bead orbit and aim sensor directly at the light. Collect brightness data and project the computer plot in real time. Let the students comment on what they are observing. Instead of swinging beads, you may use a mechanism, known as an orrery, to model the planets orbiting their star. Instructions for building an orrery from LEGO™ parts may be found on the NASA Kepler Mission website at http://kepler.nasa.gov/education/ModelsandSimulations/LegoOrrery/

I don't have Vernier light sensors but I do have the Physics Toolbox Suite on my phone which uses the light sensor already on your phone. The app is free and has many different tools all using the internal properties of your phone. I find myself using it frequently and if I ever get tablets for my classroom I'll be using this much more frequently.

I played around with the idea over the weekend using a dim kid's light and passes my hand in front of it to model a transit. At first I tried a ceiling mounted light but I found that since its a CFL bulb there were small variations in the light that might confuse students. In class I would be using incandescent light bulbs anyway. The kids' dim flashlight had a fairly consistent output and the dips were caused by my hand in front of it in a completely dark room.

I would like to model something smaller than the light source like the bead on a string that SETI suggested. It will also be a good lesson about the difficulties of the mission as students won't see too much of a reduction in light unless the shadow of the bead passes right over the sensor on the phone. I don't have orreries but can challenge students to keep constant period orbits. Perhaps by next year I can develop something super simple like this DIY Orrey.

The nice folks in charge of the @PhysicsToolbox twitter account pointed out this The Physics Teacher article on the subject sing their light sensor for something similar.

After students learn how to read Transit Light Curves from the SETI activity I hope to have them make their own and model the same graph interpreting skills. It will only take one kid with a phone in each group to make this work and I think I'll have that covered.

The Resource Area for Teaching is a Life Raft for Teachers with Limited Budgets

The Resource Area for Teaching (RAFT) was mentioned in a recent discussion on the PTSOS email list. I decided to contact RAFT to see if they could support PTSOS in some way. RAFT Site Manager Ofelia Delgadillo soon replied to my email inquiry with several ways RAFT could help PTSOS, our program for new physics teachers. I won't mention specifics here because I don't want to give away any of the surprises for those coming to the 9/17 PTSOS workshop (registration is still open). I do want to describe my experience visiting the San Jose RAFT location and how they can support physics teachers wanting to do more hands-on activities.

I easily found RAFT on Ridder Park Drive because it is a little past the Santa Clara County Office of Education. I went to the membership desk and joined. The $40 membership fee might be an obstacle to some teachers but it is only $25 to renew. If you can gather a group of 10, the new membership price is only $20 each. Many teachers should be able to get their school to pay for a membership. Either way, it will probably pay for itself on your first visit. As I waited for them to complete my registration, I noticed several teachers making use of the teacher "maker space" called the Green Room. It contains a lot of the equipment teachers need but don't always have access to like laminating machines, book binders, and button makers. After getting my membership card, I went back outside to get a shopping cart.

My first goal was to see if they had some whiteboards for modelling activities. I had to resist looking at all the lab kits as a passed through the front aisles, more on those later. I soon found several boxes full of framed 2' x 3' whiteboards donated by Silicon Valley companies. They were only $5 each. You can make your own for less money but some teachers would find that difficult and/or time consuming. The frames made them look more professional and sturdier. Many still had writing from the last time they were used. Who knows, maybe there is a billion dollar idea still on one of them! I picked out a class set of 10 of the lighter ones and navigated my now loaded cart through the back aisles. These contained art and office supplies, books, extra chachkies from corporate events, and numerous random surplus items like old VHS tape containers and biotech vials. A more creative teacher could work wonders with many of these items but I loaded up on sidewalk chalk.

In the very back is an area where volunteers work. They sort through donated items, update inventory, and package and price items. This would be an ideal place for high school students to get some community service hours. I also noticed the volunteers were assembling the lab kits that drew my attention when I entered. I decided it was time to take a look at those.

The lab kits covered many areas of science but many would be perfect for elementary, middle, and high school physics students. Each kit contains everything you need to build a hands-on device including detailed illustrated instructions, NGSS standards, "To Do and Notice" instructions à la Exploratorium, a description of the background science, and links where you can learn more. I saw many variations of old standbys like roll-back cans, hoverpucks, Benham's disks, and simple motors. There were a few intriguing ones that I was unfamiliar with like roller racers and static merry-go rounds. You can purchase single kits or lab packs of 10. The single kits averaged about $1 and the 10 packs $10. I had to restrain myself from buying them all and managed to leave with 6 of the 10-packs covering a variety of physics topics. Here are some pictures I took of the lab kit displays:

Another great resource RAFT offers is professional development. I have not participated in it but a quick look at their website shows they have a useful program worth exploring. They have scheduled workshops and will customize training for your school or district.

After taking a good look at what they have to offer I am sure you are asking, how can I get in on this? There are 2 RAFT locations in the lucky San Francisco Bay Area and one in Denver, Colorado. Sadly, the Sacramento location has closed. That is hard to believe knowing that the top supporters of education in California, the governor and the state legislature, spend a lot of time there. Perhaps the Sacramento RAFT will return in the future. If you are within driving distance of any RAFT location I highly recommend you plan a visit soon. If you are not, you are in luck, you can order many of their items online. I noticed that there were over 100 of the lab kits available plus many more items in their online store. If you are having trouble visualizing this amazing place, here is a video tour:
My only criticism of RAFT would be to maybe get a better membership card machine: