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2017 June 25

Fidget spinners revisited

Filed under: Uncategorized — gasstationwithoutpumps @ 17:55
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In Fidget spinners, I wrote about measuring and modeling the acceleration of two fidget spinners, 5-spoke spinner that cost $6.90 made from plastic and brass and a 3-bladed spinner that cost $8.90 milled out of brass:

The 5-spoked wheel spinner weighs 32.88±0.03g, and the 3-spoke brass spinner weighs 61.14±0.02g.

The previous post looked only at the fidget spinners spinning vertically (that is, with a horizontal axis), but I had noticed in playing with the spinners that they seemed to have different drag in different orientations, so I redid the measurements with the spinners horizontal (that is, with a vertical axis). I had a somewhat harder time spinning the spinners fast with them horizontally mounted, as my makeshift support for the photointerrupter was a bit precarious.

The 5-spoke wheel seemed to run smoothly , but the fit suggests more dry friction and less fluid friction.

The 3-spoke spinner really does not like to spin horizontally.

To visualize the physics better, I tried making acceleration vs. velocity plots for the fitted models:

When holding the wheel horizontally, there seems to be mainly dry friction, almost independent of the speed of the spin.

The 3-spoke spinner has much worse drag at all speeds when held horizontally rather than vertically. The fluid drag seems to be about the same as before, but there is much larger dry friction component (possibly from brass-on-brass contact between the spinner and the axle caps).

As expected from fidgeting with the spinners, the 3-blade spinner has much more drag than the wheel, both horizontally and vertically. The change from mainly wet friction to mainly dry friction for the wheel was unexpected, though.

Update 2017 Jun 25 21:15:  My wife just pointed me to a Wired article: https://www.wired.com/2017/05/the-phyiscs-of-fidget-spinners/ which does a poorer job of the same thing I did. They sampled at a fixed rate, rather than recording time stamps on each rising edge, so they had much poorer time resolution, and they assumed constant acceleration (dry friction), which is only appropriate for low-quality bearings.

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2017 June 20

Fidget spinners

Filed under: Uncategorized — gasstationwithoutpumps @ 17:34
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I recently bought two fidget spinners from Elecrow:

The 5-spoked wheel spinner weighs 32.88±0.03g, and the 3-spoke brass spinner weighs 61.14±0.02g.

The heavier 3-bladed spinner cost $8.90 and is milled out of brass (though the site claims “pure copper”, the material looks like brass and is slightly magnetic, so I’m sure it is brass).The lighter 5-spoke spinner cost $6.90.

The lighter spinner is easier to get to high speed, spins longer, has more gyroscopic effect, and has a dimple for balancing it on a pencil point, so makes the better fidget spinner in many ways.

I was curious whether I could characterize the fidget spinners electronically. I have a photointerrupter (an aligned LED and photodetector) from Sparkfun with a 1cm gap that the spinners just fit in.

Here is the 3-spoke spinner mounted in the Panavise Jr, with the photointerrupter counting 6 ticks per revolution.

Here is the 5-spoke spinner with the photointerrupter counting 5 ticks per revolution.

I set up PteroDAQ to record a timestamp on every rising edge of the photodetector, which counts 5 uniformly spaced ticks per revolution for the 5-spoke wheel, but 6 ticks (in 3 pair of closely spaced ones) for the 3-bladed spinner. I can then plot the angular position of the spinner as a function of time in gnuplot:

plot '3-spoke-spin-down-ticks.txt' u 1:($0/6.)

I tried fitting the spin-down using constant deceleration (a quadratic), using deceleration proportional to velocity (exponential decay), and using a model that has both terms: v_{0}\tau(1-e^{-t/\tau})+a t^2 /2.  I expressed position as number of turns (that being simpler to interpret than radians), and so the initial velocity v_{0}  is in turns/sec, acceleration a is in turns per second per second, and the decay time \tau is in seconds.  I got terrible fits with the constant deceleration, decent fits until the spinning got slow with the exponential decay, and quite a good fit with the combined model:

The longer spin time for the wheel is partly due to higher initial velocity, but the time constant for the decay is also much longer for the wheel, indicating better bearings.

I’m not quite sure how to interpret the slightly higher contact friction term for the 5-spoke wheel.

2012 January 20

Soldering problems

Filed under: Uncategorized — gasstationwithoutpumps @ 20:29
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In Newton’s measurement of g, I said “In preparation for this, I had bought a “photo interrupter” from Sparkfun and a breakout board to mount it. (Actually, I ordered 2, which was a good thing, since one of them did not work—Sparkfun is sending me a replacement).”

I think I owe Sparkfun a couple of bucks for that replacement, because I now no longer believe that the part was faulty.

The replacement part arrived yesterday, so this morning I unsoldered the part that I believed was faulty and put in the new one.  Getting the holes clear enough to insert the new part was a bit difficult with just a soldering iron and a solder sucker, but I eventually managed to do it.  Since I already had the good photogate set up for the physics lab, I did not get a chance to test the spare until after lab was over.  It didn’t work either!

Now, I’m willing to believe in one random part failing, but two in a row seemed unlikely.  That lead me to suspect problems with either the soldering or with the breakout board.I had already checked thoroughly for shorts (I always do that before powering up a board), and I knew there were none.

I had noticed when taking pictures of the photogate that the IR LED is clearly visible on the camera’s LCD display (strangely, it comes out looking blue, not red), so I looked at the IR diode through the camera—not lit up!  I double checked with the good part and it lit up very visibly.

I then checked the bad board for open circuits.  I quickly found that the resistor, which should be connected on one side to the ground plane was not connected to the ground pin of the header.  I re-examined all the solder joints, and one of the ones on the resistor looked a little bit less than perfect, so I reflowed the solder joints on the resistor.  Still nothing.

In desperation, I tried reflowing the solder joints on the header, although they all looked good.  Success!  It seems that the solder to the ground pad, though looking like a perfect connection, was not connecting. Now the second photogate is working just as well as the first, and I’m feeling very sheepish about having trusted visual inspection of a solder joint—I should know better than to do that.  I certainly should have done a better job of debugging before complaining to SparkFun, who were very nice about replacing the part, no questions asked.

So what can I do?  I feel I owe Sparkfun for the $1.95 part they sent me, but I’m not sure that the effort to get them the money wouldn’t cost them so much in labor costs for handling something unusual that they would lose money on my attempt to pay them.  About all I can do is encourage others to do business with them, since they seem to have real superb customer service.

If anyone does get Sparkfun’s photogate and breakout board, look at the easy Lego mounting I have in More on pendulums, which was easy to set up and worked very well. And check your solder joints carefully!

Pendulum lab went well

In today’s lab we derived the formula for the period of a simple pendulum (assuming the small-angle approximation), T= 2\pi \sqrt{L/g}, then measured both circular and simple pendulums.  For the circular pendulum we measured the radius of the cone on the first orbit and the last orbit, the length of the string (the slant height of the cone), and approximated the period by timing 10 or 20 periods and dividing.  For the simple pendulum, we used the photogate setup described in More on pendulums, to get very precise and repeatable measurements of the period.  The hardest part for us was measuring the length of the pendulums, since the center of mass for the bob was not obvious and the exact position of the pivot was not obvious—these uncertainties probably resulted in length measurements being ±5mm, making a large contribution to inaccuracy.

Here is a table of the measurements (and calculated g) we made for the circular pendulum:

Length cm radius cm num orbits period sec g cm/sec^2
 212.4  48.6–46.6 10 2.90  970.8–972.6
 212.4  38–52.4 20 2.601  959.8–974.7
 161.5  58–60.5 20 2.501  938.7–984.2

The range of estimates for g is larger than I would like.  I think that the decay of the oscillation of the pendulum makes quite a difference.  The average of all the estimates of g is 967 gm/sec^2, which is rather low.

And for the simple pendulum:

Length cm num ticks mean period sec standard deviation g cm/sec^2
207.2 47 2.8958 0.0050 975.4
171.3 74 2.6272 0.0065 979.8
95.5 89 1.9565 0.0025 984.9
54.7 58 1.4809 0.0042 984.7
28.7 44 1.0730 0.0019 984.0

The pendulum ticked reliably for quite a while, and the periods were remarkably consistent.  The estimates of g from the simple pendulum are good to about 0.5%, which is the limitation of accuracy on our pendulum length measurements and close to the limit of the accuracy of the small-angle approximation.  The average of the 5 measurements looks good to about 0.2%, which seems pretty good to me, since we certainly weren’t measuring the lengths that accurately.

I looked up the gravitational field in Santa Cruz on Wolfram Alpha’s gravitational fields widget:

total field | 9.7995 m/s^2  (meters per second squared)
angular deviation from local vertical | 0.00322°  (degrees)
down component | 9.79945 m/s^2  (meters per second squared)
west component | 3.4×10^-4 m/s^2  (meters per second squared)
south component | 0.0316 m/s^2  (meters per second squared)
(based on EGM2008 12th order model; 11 meters above sea level)

While the lab was running, one of the students wrote a Python script (using numpy for mean and standard deviation) to read the data and compute the numbers in the table.  We could have talked directly to the Arduino, but it was simpler to cut the numbers from the Arduino serial monitor and paste them into a file for the script to read. That allowed us to keep the Arduino running throughout, and just cut and paste the good numbers, discarding the junk from starting or stopping the pendulum.

I’m quite pleased with the photogate setup, which was very simple to build and worked reliably during the experiment. Crudely wrapping tape around the string made a lumpy opaque object, whose rotation probably contributed to the standard deviation of the  period—having a smoother cylinder for the optical blocker would probably make the period measurement much more consistent.  But that would not improve the mean estimates much since errors in adjacent period measurements cancel.  I believe that our mean periods are much more accurate than the standard deviations suggests, with errors less than 1 per thousand.

I had to make one change in the Arduino code during the lab to accommodate all the different pendulum lengths—I had a dead time before recognizing the next pulse, to prevent getting 2 pulses per period as the string passed through the beam twice.  I started with a dead time of 1 second, which as a bit too long for the smallest pendulum.  Reducing the dead time to 500 msec for that pendulum made it count reliably.  Note that for the 2nd and 3rd pendulum, we measured for about 3 minutes without a bad time measurement, and could have gone longer if we had had the patience.

2012 January 19

More on pendulums

In Newton’s measurement of g, I described a failed experiment to measure g with a motorized circular pendulum. Further experimentation on my own lead me to adopt for this week’s lab the standard approach using an unpowered circular pendulum.  The cone formed by the string can be described as having height h, base radius R, and hypotenuse L, the length of the string.  If the circular pendulum has period T, then g= 4\pi^2 h/T^2(derived in the Newton post).  If we make the string long and push the pendulum with the right speed to get a nearly circular (rather than elliptical) motion, then h=\sqrt{L^2-R^2} is nearly constant for many orbits, and we can estimate the period with just a stopwatch by counting 20 or 30 periods.  Using a large enough mass means that neglecting air resistance is now reasonable (which it was not for the tiny mass I started with).

Thanks to John Burk for suggesting that I forget about the motor—that seems to be the best approach, even though I then can’t use the photogate to time the period.  I’m hopeful that we can measure the height and the period accurately enough to get within about 2% of the right value for g.

This week in addition to doing the circular pendulum right, I wanted to do simple pendulums.  I’ve assigned problem 4.P.89 in Matter and Interactions, which seems to be the only place in the book that simple pendulums are done.  It is a computational problem, since there isn’t an analytic solution (though the small-angle approximation works pretty well up to about 45°).  I hope the students have done that by tomorrow!

I wanted to measure the period of the pendulum directly (not averaging over many periods), to demonstrate that the amplitude does not matter much.  Unfortunately, I’ve not yet built a sensor that works for this. I tried using the photogate, but I could not hit the 1 cm gap consistently, even with a shorter pendulum.

I also tried using a magnetic sensor (using the circuit I used for the speed-of-sound lab) with a magnet for the pendulum weight, but that triggered at random times as the magnet came close.  Even 20cm away the field was enough to trigger the detector, and I got almost random timings.  A magnetometer was no better than the coil and comparator, as the magnetic field varied chaotically (from movements of the magnet other than the simple pendulum swing, such as twirling on the string).  The magnetometer was usable as a compass, though, which is good, because I originally bought it for the robotics club to use as a compass.  There are some tricky points to using it as a compass, which I’ll talk about in a different post.

I then tried marking the top of the string with a bit of electrical tape and using the photogate there.  That was the most successful so far—if I hold the photogate steady enough, I can get readings repeatable to ±20msec, which is much better than I can do with any other approach I’ve tried.  For one pendulum hanging from the edge of my desk, I either got  two pulses at about 1.11 and 0.45 seconds or one pulse every 1.56 seconds, depending on whether the marker on the string passes all the way through the beam or blocks it continuously at the end of the swing. The random variation I get is probably because of holding the sensor by hand (to align with the string).

If I had a more rigid way to mount the sensor, I should be able get more consistent readings, so my main engineering task was to get a rigid pivot point on the ceiling beam (without making any holes) and mount the photogate in a rigid, but adjustable, way.  Of my two standard mechanical engineering techniques, duct tape and Lego, I chose Lego:

A view of the photogate mounted on the Lego beam next to the pendulum string.

Closeup of the photogate, showing the breakout board and sensor wedged between a plate and a beam, with a 2-plate spacer.

Having come up with a nice way to grip the photogate and still be able to swing a pendulum string into the gap, I connected the beam holding the photogate to the same right-angle platform that we had used last week for the motorized pendulum. This left a little gap that I could rest the Arduino board in, so that there was no tension on the wires to the photogate.

I was a bit worried that I might have to put my laptop on top of a ladder, since the USB cord is not very long, but I have a spare pair of USB-to-Cat5 converters (one set is for the robotics project), so I was able to make an extension cord out of a flexible Cat-5 Ethernet cable, giving me enough length to put my laptop safely on the desk.

The same Lego that holds the photogate can also support the Arduino, so I don't need to hold anything in my hands.

I had two other ideas I haven’t tried: using one of the ultrasonic range finders to track the pendulum motion and using a video camera to time the motion.  These require interpolation of position data to estimate the period, so I’d rather avoid them for now. The top-of-string photogate will work (I think) for the simple pendulum, and the circular pendulum can be timed with a stopwatch averaged over many periods.  (I could even use the photogate timer as a stopwatch, though the resolution of the stop watch on my Casio wristwatch is 0.01 seconds, and human reflexes make anything less than 0.1 second pretty much noise.)

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