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Flying circus of physics

Chap 1 (motion) archived stories part B

Wednesday, February 11, 2009

For Chapter 1, here is part B of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

First a list   (use "Ctrl-F" to search for a key word or just scroll down the screen)

1.56  Beds-of-nails demonstrations
1.57  Pub trick ---water and the disappearing cigarette
1.57  Pub trick --- lifting a bottle with thumb and one finger
1.57  Pub trick --- hanging spoons
1.57  Pub trick --- hanging bottle caps on your face
1.59  Pub trick --- a knot that is not a knot
1.60  Chimney climb, sometimes even cats do it
1.65  Slinky on a treadmill
1.66  Stacking blocks to get an overhang
1.67  Stabilizing the leaning tower of Pisa
1.68  Domino amplifier
1.68  Really big domino amplifiers
1.68  Human dominos for your next dull party
1.68  More domino tricks
1.69  Demolition of tall chimneys can be surprising and humorous
1.71  Failure of a bridge section
1.76  Strange ball bouncing
1.77  Bounce of the ball
1.78  Nike football commercial: real or fake?
1.81  Robbie Maddison's motorcycle jump
1.81  Car jumps
1.84  Hula-hoops
1.85  Yo-yos, unusual and gigantic
1.91  Pub trick --- balancing a coin on a folded paper edge
1.92  Bull riding
1.94  The dambusters of World War II
1.94  Stone skipping on water
1.94  Golf ball skipping over water
1.97  Cats turning over to land in a fall

Reference and difficulty dots
Dots · through · · · indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

Now the stories


1.56  Beds-of-nails demonstrations
Jearl Walker
Dec 2008    A long time ago, I introduced two bed-of-nails demonstrations to physics education. One (very painful) example is shown in the following photograph …

You see me sandwiched shirtless between two beds of very sharp nails while Peter Wiley (of my publisher, John Wiley and Sons) stands on top of the sandwich. (The photograph is courtesy of Cynthia Spencer, also of John Wiley & Sons.) If you have enough resolution on the photograph, you can see that in spite of the rigidity of the top bed, it is bent at the edge of my rib cage.

When Peter Wiley stepped off the top bed of nails and then helped me get up, I felt (and maybe heard) a slight suction effect as I pulled my back off the nails on the lower bed. The nails had not pierced my skin but they had been on the verge of penetration, with skin tightly folded over the points. Detaching myself from the nails may have caused a slight rush of air into the indentations in my skin.

In the second type of bed-of-nails demonstration, I am again sandwiched shirtless between the two beds but now a concrete block is positioned on the top bed. An assistant then swings a heavy sledgehammer down on the block, smashing it and momentarily compressing the sandwich, that is, compressing me between the two layers of nails, in something resembling the “iron maiden” of medieval torture.

At the end here, I give two links where you can see old videos of me performing the two types of bed-of-nails demonstrations.

The physics of someone standing on top

When one or two people stand on me, their weight is spread over enough nails in the top bed that the force on me from each nail is insufficient to pierce my skin. The force from the nails on my back is larger, because they must also support my weight. By experimenting I discovered how much weight the people can have before I am pierced. I can roughly calculate the pressure on me from each of the bottom nails by dividing the total weight by the number of nails on my back and by the area of each point on the nails. However, the calculation is only suggestive because my body is not uniform and thus I support more weight on some nails than on others. Don't think that I go without pain, because the demonstration hurts a great deal.

Here are some more photos. In the first two, student Amanda Beach is standing on me while being steadied by M. J. Saunders, the provost here at Cleveland State University. Amanda was quite worried about hurting me (but I don’t think the provost was). The second and third photos show me doing push ups on a bed of nails while wearing gloves lined with Kevlar (sold at I could feel the points on the nails but because they did not penetrate the Kelvar, the pushups were not painful. (The photos are courtesy of T-Fiz.)


The physics of smashing a concrete block

When a concrete block is smashed on the top bed, the large block not only adds a theatrical flare to the demonstration because it shatters so nicely, but it also increases the safety in three subtle ways.

1. If I am to be squeezed hard, then the block and top bed must accelerate rapidly downward; a larger block diminishes the acceleration because of its greater mass.

2. Much of the energy in the sledgehammer goes into rupturing the block rather than into the bed's motion.

3. The fact that the block disintegrates means that the collision time (from the start of the collision to the end) is longer than if the sledgehammer hit the top bed directly. That means that the force in the collision is smaller than with a direct hit.

Both bed-of-nails demonstrations hurt and are potentially harmful, especially the one with the sledgehammer because the face can be damaged by the debris from the concrete block. I have had some scary and also some silly moments with the demonstrations. Here are some of the stories.

First time with the smashing demonstration

The first time was in a classroom. I asked one of my students to swing the sledgehammer, but quite unwisely I had him place a common small brick on top of the sandwich of nails. I told him to hit the brick hard, covered my face with one hand, and then gave him a count of 1…2…3 so that I could brace my abdomen for the impact. The student hit the brick very hard with the sledgehammer, so hard that I lay stunned on the floor for several minutes. The students in my class were shocked, but my primary thought was that this was a stupid way to die. However, the advantage of using a large concrete block was suddenly very obvious to me. Pain has a way of rapidly clarifying the physics principles.

The smashing demonstration at Oxford University

One summer I gave the Flying Circus of Physics talk at Oxford University in England to a meeting of education experts from around the world. Unfortunately, only few in the audience spoke English, much less understood my Texas-brand of humor. So, as the talk went on and I generate only slight laughter at my jokes, I became more nervous and less cautious.

When I got to the bed-of-nails demonstration at the end of the talk, I discovered that I had to perform the stunt on a bench so that everyone could see it. My assistant put the concrete block on top of the bed sandwich and then swung the sledgehammer down on the block. Because I knew that, with this unusual arrangement, the angle of swing was awkward for the assistant, I tried to steady the top bed by grabbing it firmly with one hand. When the sledgehammer hit the block, the impact drove a nail across my hand, cutting it.

I didn't realize that I had been cut until I stood up to give my closing remarks, but then the blood flow was noticeable to both me and the audience. The audience was impressed with the demonstration and especially the blood --- they required no grasp of English to know that I had hurt myself.

After packing up the equipment, I met my host at a local pub for a pint of ale, feeling somewhat relieved that at least the final demonstration of the talk had impressed the audience. Then my host told me that the disease tetanus ("lock-jaw") was a real concern in that part of England. I had not minded the pain of the cut, but the thought of contracting tetanus worried me. (The bacteria causing tetanus enters the body through a cut from, say, a dirty nail. If the bacteria are not stopped, the victim soon dies while every muscle in the body in full contraction, unable to breathe.) I put down the pint of ale and hurried over to the local hospital for a tetanus shot.

There I had to explain to the nurse how I had cut myself. As she drove the needle into my rump, she was laughing so hard that she shook. I had traveled across the Atlantic Ocean to impress educators and had ended up dropping my pants in front of a nurse laughing at me.

Demonstration at a girl’s school

Equally embarrassing was the time I gave the bed-of-nails demonstration at an all-girls high school. I figured that the woman who invited me did not want to see the sledge-hammer part of the demonstration, so I planed to do only the part where I am sandwiched in the two beds of nails with a person standing on top. Over the phone she agreed to be that person.

What I did not think about during the phone conversation was the clothing that she should wear. I did not think about that feature until I was sandwiched in the two beds with the woman about to get on top. She was wearing a short skirt and, while standing immediately next to my head, decided to talk to the audience about what she was going to do. I did my very best to turn my face to the audience instead of looking upward; the girls in the audience went wild with laughter; the woman never understood what the problem was; and I was unable to straighten out my neck for a week.

Demonstration at IBM conventions

I used the bed-of-nails demonstration not only in class and in my Flying Circus talk, but also in a series of motivational talks I gave to sales people of IBM. I began the motivational talks by being the stereotype physics professor (talking of grand things, being as boring as possible) and then slowly dropping the talk into slap-stick and then ending with the bed-of-nails demonstration. My message was that I sell a product (physics) to people (students) who often do not initially want the product, much like the sales people try to sell their IBM product to customers who may not want the product.

In part of the slapstick I did a pratfall on the stage and fell over the edge of the stage to the floor. This stunt looked like a huge mistake, and every one of the 1000 people in each audience froze with tension when I did it because mistakes are never ever supposed to happen at an IBM presentation. Only gradually would the audience realize that the fall was planned, and then for the rest of my talk they would laugh and even cheer at my stunts.

Before each of these talks I met the leading IBM executive that was there, because he was to be the one who would stand on me when I was in the bed-of-nails sandwich. Each of these executives was concerned about hurting me. I told each, "Hey, look, this demonstration is OK. Sure, your weight is going to hurt me by pressing the nails into me, but the pain is something I can endure while you are up on top. Don't worry; I've got this figured out."

At one talk the executive was especially worried because he weighed about 230 pounds, which would put me at the limit of the pain I could endure. Nevertheless, I went through my calming words. Unfortunately, when I did my pratfall during that talk, I broke a rib as I hit the floor below the stage. At the time, I did not know that a rib was broken; I only knew that my chest hurt like crazy. I continued the talk, doing the rest of the slapstick while not breathing very well. Then came the bed-of-nails demonstration and the 230-pound executive. When he stood up on the top bed of nails, the pain in my chest went ballistic and, though I could hardly breathe, I said my routine words about the stunt.

I was back in Cleveland and at my doctor's office later that day. She told me that I had broken a rib and that I should take life easy for a month. I tried to laugh (but couldn't) and said, "You've got to be kidding. I have to be back at the IBM talks next week." And I was. But thankfully the next several executives that stood on me each weighed less than 230 pounds.

Blood all over me

Once when I gave the Flying Circus talk at Western Illinois University, my assistant could not make the trip and I asked my host if he would swing the sledgehammer down on me during the final demonstration. I told him to not be timid about the swing because that would disappoint the audience. I wanted a dramatic ending, and he gave me one. He swung that sledgehammer down hard, really jarring me. However, he came in at angle that sent most of the chunks of the concrete block across my face. I had one hand guarding my teeth and eyes, but one of the large chunks cut across my exposed chin.

When I climbed out of the beds of nails and stood up to give my closing remarks, blood poured from my chin onto my pants and shoes. My host was pale with worry, but the audience was crazy with applause. That ending was the best ending I ever had with the Flying Circus talks, and at every later Flying Circus talk I secretly hoped to be cut like that again. As I said once, a long time ago, "There is no better demonstration than one in which the teacher may be hurt or killed."

To see my bed of nails demonstrations on video, go to

and click on videos in the menu and then scroll down to the last video, which shows my appearance on The Tonight Show with Johnny Carson. To see a more dramatic video (with a sledge hammer and a cinder block), click on the second thumbnail in which you can see "Kinetic Karnival."

1.57  Pub trick --- water and the disappearing cigarette
Jearl Walker
July 2008
Here is a simple sleight-of-hand magic trick in which a cigarette disappears and then reappears. (You can substitute similar objects to avoid cigarettes.)

The saliva causes the paper on the cigarette to cling to the thumb, the same effect you might use if you wet your fingers (with either water or saliva) in order to use them to turn the page of a book.

But doesn’t that seem wrong? If you have ever slid down a water slide, you know that water is a lubricant that can almost eliminate friction. Indeed, one reason why ice is dangerous to walk on is because it is nearly always covered with a thin layer of water that makes the ice covering very slippery.

However, when water forms a very thin layer between two surfaces, especially if it can penetrate into the surfaces, it cannot flow and then it acts as a glue instead of a lubricant. When you wet your fingers to turn a page, part of the water penetrates into the spaces between the wood fibers in the paper. The water molecules not only bond to each other, but they also bond to the fibers and to your skin. Thus, the paper clings to your skin.

You can see the same physics if you dampen a small section of paper and then put into a dry ceramic bowl. The paper clings to the bowl. If you next increase the water level in the bowl, the paper is easily moved because then water can flow between the paper and the ceramic.

1.57  Pub trick --- lifting a bottle with thumb and one finger
Jearl Walker
Aug 2009 Here is the challenge: stand an empty glass bottle upside down on a table and then pick it up by placing one finger on the top (actually the bottom surface of the bottle) and the thumb on the side of the bottle, in a pinching motion. Try it and you’ll find that your finger and thumb merely slide along the glass surfaces, coming together at the edge. Even if the bottle is free of condensation, you still fail to pick it up. Here is a video that reveals the trick:

And here is the physics: Your finger and thumb are naturally lubricated with secreted oil. Even if you cannot sense the oil, it lies on the epidermis.

When you pull your fingers and thumb parallel to the glass surface, you want the static friction to prevent any sliding but static friction has an upper limit. If you exceed that upper limit, your thumb and finger slide, and that is what happens.

The upper limit depends on two factors: (1) how hard you press against the surface and (2) how much the two surfaces bond in what is called cold-welding. That bonding is due to the molecular attraction between your finger molecules and the glass molecules at the various points where the two surfaces touch. Instead of considering such molecular bonding (which we cannot actually see), we just assign an experimentally determined coefficient of friction to any two surfaces. If there is almost no bonding, the coefficient is almost zero. If there is a lot of bonding (as you would find when rock climbing shoes are pressed against rock), the coefficient is high, maybe 1.2 or so.

When you initially attempt to pick up the bottle, the coefficient of friction between the glass and your skin is probably around 0.3, a fairly low value. As you naturally pinch your thumb and finger to pick up the bottle, you press hard against the glass surfaces, but the low coefficient of friction means that the upper limit to the static friction is low. Thus, you easily exceed that limit, and then your fingers slide.

If you remove the oil from your fingers (by allowing leather or cloth to absorb it or by rubbing it off with a napkin with rubbing alcohol), you remove most of the lubrication, increasing the coefficient of friction to 0.8 or so. Then the upper limit to the static friction is high and your pinching action is not enough to cause the skin to slide over the glass surfaces.

I find the adhesion and lifting is easier if I put my thumb on the top surface and my first finger on the rear side of the bottle and then adjust their orientation to make as much contact as possible (without trapping the bottle against my palm, which would not be fair).

You can also increase the coefficient of friction by a counterintuitive trick ─ you breathe onto your fingers, depositing a thin layer of moisture. Water is a good lubricant when the layer is thick enough that the water can easily move, but a very thin layer is a good adhesive because it can bond to a surface. Here the moisture bonds to both the skin and the glass, allowing you to pick up the bottle.

1.57  Pub trick --- hanging spoons
Jearl Walker
Nov 2009 Clean a lightweight spoon and the skin on your nose, breathe lightly onto the interior surface of the spoon’s bowl and then hold it so that the surface rests against your nose. Test for adherence by repositioning the spoon and partially releasing it. When you feel it hold, let it go. There, just what you’ve always wanted: A spoon dangles from your nose. Who can resist you now? 

Why does the spoon hang? How does breathing on it first help? Can you hang spoons from other parts of your face, or, if you’re into that kind of thing, from other parts of your body?

How long can you hang a spoon from your nose? I have long claimed that my record is 1 hour and 15 minutes, set in a French restaurant in Toronto. However, the truth is that it was actually in a truck stop in Youngstown, Ohio, where a burly member of a motorcycle gang suggested that the spoon would hang better if he reshaped my nose.

Spoon hanging has probably been practiced in pubs for as long as there have spoons and pubs. There is something a few pints of beer that makes spoon hanging compulsive. As always with the pub tricks here at the FCP site, I lay down this challenge --- anyone can do a pub trick but can you explain how it works? Well, here is the physics behind spoon hanging,

If the spoon and your nose are free of oil, there can be enough friction between the spoon and the skin to hold the spoon in place. The spoon is stable provided that the center of its mass distribution lies along a vertical line through the region where it sticks to your nose. Otherwise, gravity rotates the spoon when you release it, and the motion may cause the spoon to slide off.

Condensation from your moist breath helps glue the spoon to your nose. Normally, a water layer is a lubricant because the molecule-molecule attraction is not strong enough to resist motion. For example, if you belly flop onto a water slide, the water attached to your body can easily slide over the water layer attached to the slide --- the two layers are said to undergo shearing.

However, when a water layer is very thin, perhaps only a few nanometers thick, it acts like a glue instead of a lubricant because the water can no longer be easily sheared. Instead, it is more like an elastic solid than a liquid. With the spoon trick, your breath deposits patches of very thin water on the spoon. (Patches may already be there from condensation of the room air.) When you put the spoon on your nose, these patches bind to the two surfaces. As the spoon begins to slip down your nose, the patches may yield slightly (they are somewhat elastic) but resist further sliding (they are too much of a solid to undergo shearing).

You have used this same physics if you have ever wet your fingers in order to separate the two sides of a plastic grocery bag in which you put vegetables or fruits. The bag comes off a dispenser and must be opened at one end to make way for the food, but usually the two sides are difficult to separate. Dry fingers easily slide over the plastic, but wet fingers stick enough that you can peel the two sides apart. You might lick your fingers or dip them into water sprayed onto the vegetables or fruits. Either way, the water layer is probably thick enough to be sheared. However, when you pinch the plastic between your fingers and then move in a rubbing motion, you immediately thin the water layer and then it cannot be easily sheared. The increase in friction between your fingers and the plastic allows you to rub the plastic layers in opposite directions, opening up the bag.

If you hang spoons (either just you or a group or a class), send me a photo and I’ll post it here. Or, you could post it on your FaceBook site and then “friend me” so that I can see it. However, no spoon-hanging while driving a car or you will end up part of this month’s lead story about cars crashing into shops.
photo credits: above left, Cynthia Spencer of John Wiley & Sons; above right, Richard Howard, for the Smithsonian Magazine.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Zwicker, E., "Doing physics," Physics Teacher, 20, 181-182 (1982)
· Martin, J., How To Hang a Spoon, Turnbull & Willoughby Publ., 1985
· Wolkomir, R., "'Old Jearl' will do anything to stir an interest in physics," Smithsonian, 17, 112-121 (October 1986)
· Walker, J., "Hanging a spoon from the nose," Physics Teacher, 25, 216-217 (1987)
·· Jinesh, K. B., and J. W. M. Frenken, “Capillary condensation in atomic scale friction: How water acts like a glue,” Physical Review Letters, 96, #166103 (4 pages) (28 April 2006)
·· Feiler, A. A., J. Stiernstedt, K. Theander, P. Jenkins, and M. W. Rutland, “Effect of capillary condensation on frition force and adhesion,” Langmuir, 23, 517-522 (2007)
·· Cai, S., and B. Bhushan, “Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles,” Philosophical Transactions of the Royal Society A, 366, 1627-1647 (2008)
·· Kim, D-I., J. Grobelny, N. Pradeep, and R. F. Cook, “Origin of adhesion in humid air,” Langmuir, 24, 1873-1877 (2008)

1.57 Pub trick --- hanging bottle caps on your face
Jearl Walker
July 2010    Here is the first challenge: Hang a bottle cap (beer or soda) from your cheek or forehead. Of course, you could press the rough bottom edge so forcibly into your flesh so that it cuts a circular notch on which it can hang. But having a bunch of people with blood streaming off their faces and onto their clothes is usually not considered to be a “fun thing” to do at the pub.

Here’s a better solution.

Slightly wet the top of the cap with either spilt liquid or some of the condensation on the cold bottle. Then lightly press that surface onto the cheek. The cap will hang there for a surprisingly long time. The physics is the same as with the trick of hanging a spoon from your nose: A fairly thick layer of water acts as a lubricant because one layer of water can easily slide past the adjacent layer --- water cannot resist shearing. However, a thin layer acts as an adhesive because the water can form hydrogen bonds with the surface of both the cap and your flesh.

Here is the next challenge: How many bottle caps can you hang anywhere on your face before any of them fall? The image here shows six on my grandson’s face. Can you at least beat that? You can post photos at the Facebook site for The Flying Circus of Physics:!/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=wall&ref=ts

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Zwicker, E., "Doing physics," Physics Teacher, 20, 181-182 (1982)
· Martin, J., How To Hang a Spoon, Turnbull & Willoughby Publ., 1985
· Wolkomir, R., "'Old Jearl' will do anything to stir an interest in physics," Smithsonian, 17, 112-121 (October 1986)
· Walker, J., "Hanging a spoon from the nose," Physics Teacher, 25, 216-217 (1987)
·· Jinesh, K. B., and J. W. M. Frenken, “Capillary condensation in atomic scale friction: How water acts like a glue,” Physical Review Letters, 96, #166103 (4 pages) (28 April 2006)
·· Feiler, A. A., J. Stiernstedt, K. Theander, P. Jenkins, and M. W. Rutland, “Effect of capillary condensation on frition force and adhesion,” Langmuir, 23, 517-522 (2007)
·· Cai, S., and B. Bhushan, “Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles,” Philosophical Transactions of the Royal Society A, 366, 1627-1647 (2008)
·· Kim, D-I., J. Grobelny, N. Pradeep, and R. F. Cook, “Origin of adhesion in humid air,” Langmuir, 24, 1873-1877 (2008)

1.59  Pub trick --- a knot that is not a knot
Jearl Walker
December 2012 Take two long plastic straws. Let’s say that one is red and the other is white. Wrap the red one around the white one as shown here.

Then wrap the white one around the red one as shown here.

Hold the two adjacent ends of the white one in one hand. With the opposite hand, pull the ends of the red ones together on the opposite side.

You should then have a sturdy knot because the two straws are each completely wrapped around each other. However, watch this:

Why can the knot be so easily pulled apart?

In the final arrangement, the red straw forms loop A around loop B in the white straw. If you slightly wiggle and twist the straws, loop A can slip over loop B, and then the straws are free of each other.


1.60 Chimney climb, sometimes even cats do it
Jearl Walker
January 2014  When climbing a wide crack on a mountainside you might be able to chimney climb by pressing your shoulders against one wall and your feet against the opposite wall. I used the technique in climbing down shafts while cave exploring. Here is a figure from my textbook Fundamentals of Physics and also from The Flying Circus of Physics that shows the general orientation.

You are stable as long as your forces on the rock are large enough, but the procedure is tiring, especially because you are afraid of falling and thus push extra hard. However, in 1976 two mechanical engineers published calculations that showed that there a way to reduce the forces (and thus the fatigue) by properly positioning your feet. In principle you can find the position of least effort by first putting your feet at some low position and then decreasing your push until the feet are on the verge of slipping. If you then raise your feet while continuing to keep your feet close to slipping, you further diminish the required push. However, the action increases the friction required at the shoulders because the friction at the feet is now less, and the sum of the frictional forces must always equal your weight if you are not to fall. If you continue to shift your feet upward until your shoulders are also about to slip, you are then in the position that requires the least push against the rock.

If you would like to see the full calculations, find the original article by Hudson and Johnson. Their calculations are not limited to just humans climbing. They also apply to this cat as it chimney climbs down between a refrigerator and a wall, except there are four legs pushing against a surface instead of two.

When the cat pauses, I think it must be mentally recalculating the forces needed to give it enough friction in spite of the smooth refrigerator surface. Cats love physics. (Well, maybe not Schrödinger’s cat.)

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
·· Hudson, R. R., and W. Johnson, "Elementary rock climbing mechanics," The International Journal of Mechanical Engineering Education, 4, 357-367 (1976)
· Walker, J., "The mechanics of rock climbing, or surviving the ultimate physics exam" in "The Amateur Scientist," Scientific American, 260, 118-121 (June 1989)


1.65  A slinky on a treadmill
Jearl Walker
May 2012 A Slinky is the well-known spring toy of Poof-Slinky, Incorporated, that can be made to climb down (somersault down might be a better description) a flight of stairs.

You place the spring on the highest step, pull the top of the spring up and then down onto the second step, and then let go. Provided the step dimensions are appropriate, the Slinky then climbs down the steps until it reaches the bottom of the flight. The time the Slinky takes to climb down a flight depends on the number of steps it takes (you might arrange it to take the steps two at a time) but is independent of the height of each step. (A Slinky climbs down a tall step and a short step in the same time.)

When you pull the coils up and then down onto the lower, second step, you send a wave through the length of the coil. As the wave travels, more coils move onto the second step by first moving upward, then along the arc of the spring, and then down onto the second step. When the wave reaches the last coils on the first step, those coils are pulled up with enough speed along the arc that they overshoot the second step and (provided the step dimensions are appropriate) land on the third step. The whole process is then repeated.

A Slinky’s success in climbing down stairs (and slowly enough that you can see the climbing) is due to the rectangular cross section of its wire. That design, patented by Richard T. James in 1947, reduces the ratio of the spring’s stiffness to its mass compared to wire with a circular cross section. The smaller ratio results in a slower speed for the wave you set up along the length of the spring. A plastic Slinky, with a different ratio and thus a different wave speed, climbs about half as fast as the original steel-wire Slinky.

With either type, the time required for a Slinky to climb down one step is set by the ratio of stiffness to mass, not the height of the step. On a short step, the wave travels slowly; on a tall step, the wave travels faster; and the time required by the wave to travel the length of the Slinky is the same for the two steps.

Half a century after the invention of the Slinky, someone has realized that they can walk along a moving treadmill:

As the coils are pulled up along the arc, the base of the Slinky is being pulled toward the rear of the machine. The result is that the base is pulled out from under the last of the coils climbing over the arc, and so those last coils land forward of the base, forming the new base. And then the whole process continues. Brilliant. 

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
·· Cunningham, W. J., "The physics of the tumbling spring," American Journal of Physics, 15, 348-352 (1947)
··· Longuet-Higgins, M. S., "On Slinky: the dynamics of a loose, heavy spring," Proceedings of the Cambridge Philosophical Society, 50, 347-351 (1954)
· Burger, W., "Slinky zum 40. Geburtstag," Physikalische Blatter, 42, 407-408 (1986)
·· Burger, W., "Ode to Slinky on its birthday," The Science Teacher, 54, 25-28 (October 1987)
· Cunningham, W. J., "Slinky: the tumbling spring" in "Marginali," American Scientist, 75, 289-290 (1987)
· Webb, G. N., and W. J. Cunningham, (letters) "Origins of Slinky," American Scientist, 75, 457 (1987)
·· Chokin, D., "Slinking around: put some spring in your walk -- and vice versa," Quantum, 3, 64-65 (November/December 1992)
··· Hu, A-P., “A simple model of a Slinky walking down stairs,” American Journal of Physics, 78, No. 1, 35-39 (January 2010)


1.66  Stacking blocks to get an overhang
Jearl Walker
March 2007 
  Stacking blocks to make a leaning tower has long fascinated both mathematicians and normal people, including those students who have built a tower of books that leans from a library table out over an aisle, threatening to collapse onto a careless library patron. (Don’t you dare do this. Librarians are usually calm and helpful, but if you mess with their books, they transform into the orcs of Tolkien’s Middle Earth.) The standard question is, “What is the maximum overhang?” The standard answer is, “If you stack the blocks properly, there is, in principle, no limit.”
    However, M. R. Khoshbin-e-Khoshnazar of the Physics Department at the Research Institution for Curriculum Development & Educational Innovations in Tehran recently pointed out that a practical matter limits the stacking: The bottom block gets squashed by all the higher bricks and if the number of higher blocks exceeds a certain limit, the bottom block “yields,” that is, it deforms and collapses.
    If the usual stacking scheme is followed, you put the center of mass of the top block just over the outer edge of the underlying second block. Then you put the center of mass of those two top blocks just over the edge of the underlying third block. And so on. If a block has the physical characteristics of a standard rigid brick and a height of 20 cm, the maximum number of blocks for a stable tower is about 853 and the maximum height of the tower is about 171 m. If you switch to bricks with another height, the number of bricks is different but the maximum height of the stack does not change. Video of stacking blocks and then placing a thin rod under the center of mass of the full stack. UCLA, diagram of how to stack the blocks Photo

· · Khoshbin-e-Khoshnazar, M. R., “Simplifying modeling can mislead students,” Physics Education, 42, No. 1, 14-15 (January 2007)

Want more references? Use the link at the top of this file.

1.67  Stabilizing the leaning tower of Pisa
Jearl Walker

The famous tower in Pisa, Italy, began to lean toward the south even during its construction, which spanned two centuries. Indeed, when the bell chamber was finally added at the top, it was made vertical in the hope of arresting the lean of the rest of the tower.

In modern times, the tower was closed to tourists after a tower in Pavia collapsed, killing four people. The danger is not so much that the tower in Pisa would actually topple over like an upright domino pushed on one side. Rather, the danger was that as the weight shifted to the south side of the tower, the support structure at the south side of the base would suddenly burst under the huge compression, and then the tower would fall over.

The tilting has been due to the uneven compacting of the underlying mud, sandy soil, and clay, with one side of the support gradually giving way as the ground shifts. During the 20th century, the top of the tower moved southward at about 1.2 millimeters per year but the rate alarmingly shot up in 1935 when an ill-advised attempt was made to seal the foundation against water seepage by drilling into the cement and filling the drill holes with a cement grouting mixture.

In 1990, the Italian government set up a committee with the challenge of stabilizing the tower. The primary method was to remove small amounts of soil beneath the north side of the tower by means of a drilling rig angled into the ground. A pile of lead weights was also placed on the north side to encourage the ground there to slump. Very gradually the tower began to rotate back northward. However, the situation was so touchy that the tower’s motion was briefly affected by even a northerly gale and a decrease in the air temperature.

The soil removal was stopped in 1999 and the lead bars were gradually removed. Last month the committee in charge of the stabilization announced that the tower is now stabilized and should remain stable for a very long time, standing ready for the countless photos that tourists will take of it.

· Covington, R., “The leaning tower straightens up,” Smithsonian, 32, No. 3, 41-47 (June 2001)
· Barends, F. B. J., “A Dutch leaning tower saved in 1866 by the same method used for the Pisa tower,” Geotechnique, 52, No. 2, 141-142 (2002)
· Burland, J., M. Jamiolkowski, and C. Viggiani, “Preserving Pisa’s treasure,” Civil Engineering, 72, No. 3, 42-49 (March 2002)
· Burland, J. B., M. Jamiolkowski, and C. Viggiani, “The stabilization of the leaning tower of Pisa,” Soils and Foundations, 43, No. 5, 63-80 (October 2003)

Want more references? Use the link at the top of this page.

1.68  Domino amplifier
Jearl Walker
March 2009    A common pastime is to arrange upright dominos in a line so that when the first one is knocked over, a chain reaction is sent along the line. Although videos involving thousands of dominos are available on the web, the most impressive display I have ever seen was described in a paper published in 1983 by Lorne Whitehead of British Columbia. He called his arrangement a domino amplifier because the chain reaction went through progressively larger dominos, each one 1.5 times larger in each dimension than the preceding one. Here is a scan of his photograph of the dominos.

He toppled the first, very small domino by “nudging it with a long wispy piece of cotton baton.” It then toppled the next domino and so on, until the 13th domino fell. As Whitehead pointed out, if he had continued the series to 32 dominos, the last one would have had a height comparable to that of a skyscraper. Thus, the slight nudge on the initial tiny domino would have resulted in toppling a gigantic block. (This would be a splendid metaphor for how we got into our current economic crisis.)

If we set up a normal domino line, we do a certain amount of work in lifting each domino to its upright position against the downward pull of the gravitational force. Our work is said to result in a gravitational potential energy associated with the elevated center (or center of mass) of the upright domino. If we topple the domino so that the center falls, the stored energy is transferred to kinetic energy during the domino’s rotation downward and then it is transferred into sound, vibration, and some very slight heating during the domino’s collision with the floor.

In a normal domino toppling demonstration, each domino hits another domino before reaching the floor and thus energy is transferred along the line, domino to domino. In each collision, some of the energy is transferred to sound, vibration, and slight heating, but much of the energy is transferred to the next domino as kinetic energy. If the dominos are identical and equally spaced, a steady amount of kinetic energy moves along the line, from domino to domino.

However, in Whitehead’s arrangement the amount of kinetic energy increases along the line (it is thus amplified). The increase is due to the progressively larger gravitational potential energy associated with the progressively larger dominos. That is, each domino is more massive the preceding one and has a center of mass that is more elevated than the preceding one. From one domino to the next, each dimension (width, thickness, and height) is 1.5 times that of the preceding domino. Thus, the center of mass is 1.5 times higher than that of the preceding domino. And the volume (and thus the mass) is 3.375 (= 1.5 x 1.5 x 1.5) times that of the preceding domino. Therefore, the gravitational potential energy (which depends on the mass and the height of the center of mass) is 5.06 (= 1.5 x 3.375) that of the preceding domino.

Here are some results:

2nd domino has 5.06 times the energy of the 1st domino.

3rd domino has 5.06 x 5.06 = 5.062 = 25.6 times the energy of the 1st.

10th domino has 5.069 = 2,100,000 times the energy of the 1st.

13th domino has 5.0612 = 280,000,000 times the energy of the 1st.

Also, as Whitehead pointed out, the energy released by that last domino is about 2 billion times the energy needed to nudge over the first domino. Of course, the energy does not come for free because someone must do work to put the dominos in their upright positions. And if the last block is as tall as a skyscraper, the work would be enormous. Still, even Whitehead’s arrangement of 13 dominos was very impressive when the last domino fell over with a mighty thud soon after I nudged over the first, tiny domino with only a slight touch. I must admit that I felt very powerful, well, for a minute or two until I faced the task of lifting all the dominos back into their upright positions.

My article about the physics of dominos and the domino effect is the “Article of the month” here at this FCP site.

Here are other sites: Paul Doherty’s instructions about constructing the demonstration, from the Exploratorium in San Francisco, California scanned copy of Lorne Whitehead’s original publication in American Journal of Physics


· Daykin, D. E., "Falling dominoes," Problem 71-19, SIAM Review, 13, 569 (1971)
··· Shaw, D. E., "Mechanics of a chain of dominoes," American Journal of Physics, 46, 640-642 (1978)
· Speco, B., Jr., with B. Sugar, The Great Falling Domino Book, Warner Books, 1979
·· McLachlan, B. G., G. Beaupre, A. B. Cox, and L. Gore, "Falling dominoes," solution to problem 71-19, SIAM Review, 25, 403-404 (1983)
· Whitehead, L., "Domino 'chain reaction'," American Journal of Physics, 51, 182 (1983)
· Walker, J., "Deep think on dominoes falling in a row and leaning out from the edge of a table" in "The Amateur Scientist," Scientific American, 251, 122-130 (August 1984)
··· Bert, C. W., "Falling dominoes," SIAM Review, 28, 219-224 (1986)
··· Stronge, W. J., "The domino effect: a wave of destabilizing collisions in a periodic array," Proceedings of the Royal Society of London A, 409, 199-208 (1987)
··· Stronge, W. J., and D. Shu, "The domino effect: successive destabilization by cooperative neighbours," Proceedings of the Royal Society of London A, 418, 155-163 (1988)
··· McGeer, T., and L. H. Palmer, "Wobbling, toppling, and forces of contact," American Journal of Physics, 57, No. 12, 1089-1098 (December 1989)
··· van Leeuwen, J. M. J., “The domino effect,” (2004) available at arXiv:physics/0401018v1
··· Efthimiou, C. J., and M. D. Johnson, “Domino waves,” (2008) available at arXiv:0707.2618v1
·· Larham, R., “Validation of a model of the domino effect," (2008) available at

1.68 Really big domino amplifiers
Jearl Walker
Nov 2010  In 1983, Lorne Whitehead, now at the University of British Columbia, published a paper about a domino amplifier. It was so impressive that almost immediately I described his demonstration in one of my monthly articles for Scientific American.

In the normal domino effect, you store energy by lifting the identical dominos to their upright orientation and then you send a pulse along the line by toppling the first domino. As the pulse moves, it converts the stored energy to kinetic energy (the falling of the dominos), sound waves (you can hear the collisions between dominos), and thermal energy (the dominos rub against each other as they fall). On the average, the pulse is unchanged as travels along the line.

Whitehead’s domino amplifier is different in that the first domino is tiny and the rest are each scaled up from the previous one by 1.5 times in each dimension. Whitehead nudged over the first domino with a cotton swab (Q-Tip). Even though the first one is small, its collision with the second domino is enough to knock over the second one. Then there is enough energy in the second domino to knock over the third one. As the toppling moves along the line, the progressively larger dominos fall over. The fall of the last one (the 13th in the line) is ponderous. The whole chain of events seemed impossible --- how could a slight nudge from a cotton swab result in such a resounding final thud that could almost be felt through the floor?

Videos of Whitehead’s design have now made it to video.

There is no theoretical limit to the size of the last domino. Indeed, it could be as tall as a building.

The only limitations are practical ones: How large a crane do you need to lift the last, big dominos into their upright positions, and how can you guard against them accidently falling and killing someone? Here are video links to some of the more dramatic attempt at setting a world record: News Item: Largest Toppling Domino Stone World Record: Largest Toppling Domino Build Up Transition from the traditional domino toppling to a domino amplifier

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Whitehead, L., "Domino 'chain reaction'," American Journal of Physics, 51, 182 (1983)
· Walker, J., "Deep think on dominoes falling in a row and leaning out from the edge of a table" in "The Amateur Scientist," Scientific American, 251, 122-130 (August 1984)


1.68 Human dominos for your next dull party
Jearl Walker
Dec 2009    Here is some physics for your next party, especially if it is deadly dull. Set up a chain of human dominos in which the physics of instability is demonstrated by the party goers, one after another, as in this video from the Blue Peter show in the UK.

They use mattresses but finding a mattress for everyone at a party is not very practical. So, instead, you could just following the guide of this prank:

The idea for such toppling comes from the domino effect, in which dominos in a line are made to fall one after another after the first in the line is nudged over. As each domino falls, it trades in gravitational potential energy for kinetic energy, so that it forcibly strikes the next domino, making it fall, and so on. Setting up huge displays of falling dominos has become great sport, as in this video, where over four million dominos are toppled to set a new record.

I must admit that I get nervous watching such displays, knowing that people have spent thousands of hours setting up the dominos and yet the toppling may reach a bad spot along a chain and stop.

In spite of my nervousness, I am fascinated by the repeated clicking made by the dominos as they strike one another. The frequency of the clicking is a measure of how fast the toppling wave (or toppling effect) sweeps along the line of dominos.

Suppose you have a very long line of equally spaced dominos. Once you begin the toppling, the wave initially accelerates and then settles down to a constant speed, and thus a constant frequency of clicks. That constant speed depends on the spacing between the dominos. A closer spacing results in a greater value for the constant speed, because each domino reaches the next one after only a short fall. A greater spacing requires each domino to fall farther to reach the next one, and that means that the wave moves slightly more slowly along the line.

Ron Larham has posted descriptions of how he was able to measure the speed of the waves by recording the clicking frequency with a Windows sound recorder, running under Windows 98. Because the recording picks up lots of noise (even from the room lights), he needed to do a Fourier analysis of the recorded data to pull out the dominant frequency of the domino clicking and calculate the speed. Here are his posted descriptions.

You already have an intuitive feel for the speed at which a toppling wave should move along a line of dominos. If it were to move much slower, you would immediately know that something was wrong, even though you may not immediately realize that it is the speed that is wrong. Here is an example in which the dance group The Rockettes play with our intuitive feel for toppling speeds, to amuse us.

Now that I have related clicking frequency and the speed of the wave, watch these mattress domino videos. You won’t hear clicking (because mattress are soft and yielding), but you can still measure the speed by the frequency of grunts and squeals of the people as they fall over, one after another. Bid for mattress domino record Spanish TV show

And if you have lots of time to kill (for example, you are looking for an excuse not to study for that dreaded Pchem exam) and want to set up a toppling demonstration but are tired of dominos, how about vacuum cleaners, coins, shoes, DVDs, portraits, slices of toast, and almost everything else you can find around the house, as in this video:

There you go. Now you have the perfect reason not to study for the exam --- you are simply too busy doing a physics experiment. If you post a video, send me word and I’ll put a link to it here.

More: beer commercial World Record human domino 145 mattresses CD discs on Blue Peter TV show over four million dominos
1.68 More domino tricks
Jearl Walker
April 2011 It is time for another round of domino tricks, but most of these go beyond the simple linear examples of the domino effect. In the first one, an empty soda can is propelled along the line of dominos by repeated impacts from the falling dominos. It rides the wave of falling dominos almost like a surfer being propelled by an ocean wave. pushing a can

In The Flying Circus of Physics book I present several domino stacking schemes in which you can extend an arc of dominos out from the edge of a table. The idea is that the center of mass (the center of the mass distribution in the stack) is located at least slightly above the table, slightly in from the edge. We can say that the gravitational force acts at the center of mass, pulling downward of course. If the center of mass were out beyond the edge, that force would cause a torque that would rotate the stack around the edge and onto the floor.

Here is another stacking scheme that caught me by surprise: a number of dominoes are supported by a single domino. single support even larger stack on a single support

The point here is that the center of mass of the stack is located above the supporting domino. The gravitational force pulls downward but without creating any torque. If the stack were to lean off to the side, bringing the center of mass out beyond the supporting domino, the stack would simple fall.

When domino toppling really got going (probably due to YouTube and other video outlets), the challenge was to set up long lines of dominos, in which each domino would fall against the next one. The toppling was due to both the impact and the fact that the gravitational force would exert a torque on the domino once its center of mass was no longer over the support area. However, the constraint of the room meant that the line would have to be turned. In the early days, the turning was accomplished by slightly skewing each domino from a straight line arrangement. These days there are other ways of turning the toppling. Here is one novel way with a spare light bulb:

And here is a technique called the split that sends dominos off at an angle: the split many splits

Here are schemes to make the toppling turn by 90 degrees, or to have the dominos fall in the direction opposite the direction the wave is traveling, or to have them fall off to one side. turning 90 degrees, making dominos fall in the direction opposite the wave of toppling or off to one side of the wave

In the normal schemes, the dominos all fall down, but you can arrange for some of them to fall up. making dominos stand up turning 90 degrees and making dominos stand up

And if you are not already saturated, here are a few more schemes and tricks: various tricks new domino techniques various techniques but the race toward the end is interesting. various schemes including the T arrangement. 90 degree turn 90 degree turn

I am impressed by how the little bit of physics involving the center-of-mass stability has resulted in countless hours spent by people lining up and then knocking over dominos.

For lots of references to the physics of dominos, click on
and scroll down to item 1.68.

1.69 Toppling chimneys
Jearl Walker
January 2013 When a tall chimney falls, it likely will rupture somewhere along its length. What causes the rupture, where is it located, and which way does the chimney bend after the rupture?

You can check your answer by toppling a stack of children’s blocks and noting which way the stack curves during the fall. You might also set up a stack of short, hollow cylinders that are held together internally with elastic bands.

As the chimney rotates around its base, the lower part attempts to rotate more quickly than the upper part, and the chimney begins to bend backwards. If the chimney is a uniform cylinder, the greatest attempt at bending is at a height of the chimney’s height, and so the chimney is most likely to rupture there. If a chimney has some other shape, the rupture point will be elsewhere. The rupture begins to travel across the width of the chimney from the front of the fall, but the compression on the back side drives the crack downward somewhat. A second break point sometimes occurs lower on the chimney as the top part attempts to slide backwards over the bottom part, thus pulling against the fall on the upper surface of the bottom part.

Here are some video examples: Florida Power & Light Company, both stacks break Kennecott Smelters, at least one breaks four stacks, at least two break but dust hides the last two

Sturdy chimneys can withstand the stresses during the fall and avoid breaking. Here are a few examples. My favorites are, of course, where a chimney falls the wrong one. chimney does not break but falls the wrong way, Ohio truck attempts to torque chimney over but ends up oscillating the chimney enough that it fell the wrong way. Ohio Edison, chimney falls into power array does not break but falls wrong way onto building and train track

Today most chimneys are brought down by explosions on one side of the base. Once that part of the base is removed, the gravitational force on the chimney’s center of mass creates a torque that rotates the chimney around the remaining portion of the base. The chimney then falls toward the side of the explosions. So, by careful placement of the explosions, you should be able to control where the chimney hits. However, as you can see in the preceding videos, the plan does not always work. One reason is that multiple explosions around the base may not go off simultaneously, and the first might then allow the chimney to fall off at angle to the intended direction.

A far more scientific way to bring down a chimney is to carefully remove some of the bricks on one side of the chimney base while wedging in lumber to maintain support for the rest of the chimney. When enough bricks have been replaced, you light a fire so that the supporting lumber eventually burns and breaks. Then the chimney falls toward that side where bricks had been replaced.

This was the technique used by the legendary Fred Dibnah . Here is a documentary in which he shows the technique. Although it is an hour long, it is fascinating. Note, for example, how he analyzes the cracks along the base to determine the weak regions.

More videos: San Manuel smoke stacks, at least one breaks St Paul Excel Energy St Paul a different view Fernbank Mill Chimney

Here are a few of the recent references. For the full (long) list go to
and scroll down to item 1.69 Falling chimneys, pencils, and trees .
Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
··· Varieschi, G., and K. Kamiya, “Toy models for the falling chimney,” American Journal of Physics, 71, 1025-1031 (October 2003)
··· Wilson, J. F., “Segmented impact fracture of toppling truncated cones and tall trees,” International Journal of Impact Engineering, 30, 351-365 (2004)
·· Varieschi, G. U., and I. R. Jully, “Toy blocks and rotational physics,” Physics Teacher, 43, 360-362 (September 2005); see also the material at the site
··· Cross, R., “The fall and bounce of pencils and other elongated objects,” American Journal of Physics, 74, No. 1, 26-30 (January 2006)
··· Denny, M., “Comment on ‘Toy models for the falling chimney,’ by Gabriele Varieschi and Kaoru Kamlya [Am. J. Phys. 71 (10), 1025-1031 (2003)]”, American Journal of Physics, 74, No. 1, 82-83 (January 2006)

1.71 Physics behind the tragic Mianus Bridge collapse
Jearl Walker
January 2015  A few times a year a bridge will collapse somewhere in the world, and we can always say, “Well, its structure was fatigued and should have been replaced.” But here is a bridge collapse where the physics can be described in detail.
First, a video about the collapse. The challenge here is this: Can we say anything more intellectual than a simplistic newspaper report?

June 28, 1983, Greenwich, Connecticut, USA: At 1:28 a.m., a 30 meter length of the bridge spanning the Mianus River on Route I-95 collapsed. In the dark the occupants of two cars, a tractor-trailer, and another truck failed to spot the missing section in time, drove over the exposed edge, and fell 20 meters into the river. Three people were killed and three ­others were hurt.

Bridges sometimes collapse because of age or disrepair, but that bridge on I-95 had seemed to be in good condition. Was there something odd about its design or the way in which traffic crossed it that could have led to the tragedy?

Here are some clues. Because of the angular approach the highway takes to the river, the bridge sections are diamond shaped. Each section was supported along two edges. Along the southern edge of the failed section, the support was provided by two pin and hanger assemblies, one at each corner (Fig. 1-26a).

Each assembly consisted of two steel bars through which steel pins passed. At both ends of each pin a large nut had been tightened and welded to secure the pin.

The assemblies allowed some flexibility in the bridge section so that it could respond to vibrations from the traffic load and to any variation in length from a temperature change. Apparently one of the nuts at the corner farther from the center of the section fatigued and its pin worked its way free, causing the section to fall into the river. What sideways force freed the pin? The answer proves to be a worthy study if such catastrophes are to be avoided.

Consider a truck in an outside lane as it crossed a section of the bridge. For the truck to maintain speed, its tires had to push back continuously against the section, creating a torque that attempted to rotate the section around its center (Fig. 1-26b). The attempted rotation produced a sideways force on both sets of support pins and nuts on the southern end, but the force was largest at the farther corner because of its greater distance from the center.

After considerable vibration and stress, one of the nuts at that corner failed and its pin slipped out of place, allowing the corner to drop. The diminished support of the section overloaded the rest of the support points and the section fell. Had the section been square instead of diamond, the resistance to rotation would have been shared uniformly by all four corners, and so the failure at one corner would have been less likely.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Browne, M. W., "Disaster on I-95," Discover, 4, 14-22 (September 1983)
·· Gorlov, A. M., "Disaster of the I-95 Mianus River Bridge. Where could lateral vibration come from?" Journal of Applied Mechanics ASME, 51, 694-696 (1984)
· Christie, S., and J. M. Kulicki, “New support for pin-hanger bridges,” Civil Engineering, 61, No. 2, 62-64 (February 1991)
· Levy, M., and M. Salvadori, Why Buildings Fall Down, W. W. Norton & Company, 1992, Chapter 9, ISBN 0-393-31152-X
··· Tabarrok, B., and E. Esmailzadeh, “Induced vibration of bridges traversed by moving vehicles,” Transactions of the Canadian Society for Mechanical Engineering, 24, 1B, 191-198 (2000)


1.76  Strange ball bouncing
Jearl Walker
September 2012 You might think that the bouncing of a small ball is so commonplace as to be boring, but here is an act by Michael Moschen that has intrigued me for several decades. Basically, he throws an elastic ball inside a large vertical wooden triangle, but instead of the ball simply bouncing in a random direction, Mohsen knows exactly where it will be after two or more bounces. How can he know that? Well, the answer is that he has worked out the physics of the bouncing. Michael Moschen performs the triangle same video

The bounce of the ball from a board on the side of the triangle is much like the bounce of a pool ball from the cushion along the side of a pool table and the reflection of a light ray from a flat surface: The angle of the bounce (or reflection) is equal to the angle of incidence, both measured relative to a perpendicular line to the surface. That perpendicular line is called the normal. As you watch the video, notice that Moschen throws the ball down at the horizontal, bottom board at an angle 30 deg to the normal and thus parallel to the slanted board at our left.

The ball bounces at an angle of 30 deg and then travels up to the slanted board, where the angle of incidence is again 30 deg and so is the angle of bounce.

All that means that the ball leaves the slanted board at our left by traveling horizontally across the triangle. Moschen can grab it then or let it bounce from the board at the right and go through one more bounce. Those bounces at the right side reverse the sequence of bounces at the left side, and the ball finally heads back up to Moschen at the same angle that he initially used to throw it down.

Of course, the paths are slightly curved because of the gravitational pull on the ball while it is in flight, but the curvature is not enough to disrupt the final catch.

Super Ball

A toy from the 1960s has reappeared. The Super Ball, which is a highly elastic rubber ball from Wham-O, Inc., bounces extremely well, with little loss of energy in each bounce, because of its construction. Because it bounces so well, it can behave in strange ways. You can see the difference in this next video. First, several common elastic balls are thrown underneath a table. They tend to move in the forward direction, bouncing between the table and floor until they run out of energy. Then a Super Ball is thrown under the table. Notice where it goes. superball bounce underneath table

As I explain in The Flying Circus of Physics book, when a normal rubber ball hits, the sudden compression on its lower side causes the ball to oscillate. The time for one oscillation depends on the material makeup of the ball. Chances are that the time differs from the time required for the full collision, in which case the ball continues to oscillate after it has left the floor. The oscillations require energy, and so the ball then has less energy for its upward travel and does not go particularly high.

A Super Ball consists of a core that is surrounded by a shell of different material. The construction alters the oscillations so that the time taken by the first one matches the time the ball is on the floor. Just as the bottom of the ball is reversing its compression and shoving off from the floor, the oscillation is outward against the floor, and so it helps launch the ball. As a result, the oscillation’s energy is put back into the upward motion of the ball, allowing the ball to go high.

The oscillations and reduced loss of energy also increase the magnitude of the frictional force acting on the ball when it bounces from a surface. That force then alters the angle of bounce. If the ball is thrown downward on a horizontal surface toward our left, the frictional force on the ball (which attempts to stop any sliding toward the left) points to our right.

That force decreases the angle of bounce, and the ball leaves the surface along a path that is closer to the vertical than its initial path. Here is a slow-motion video that shows the change in path. Notice that the frictional force also causes the ball to rotate counterclockwise.

During the ball’s contact with the table’s underside, both its leftward motion and its counterclockwise rotation tend to slide the ball against the surface. A rightward frictional force prevents the sliding, but then that rightward force sends the ball off to the right and with a clockwise rotation.

This is quite different from the travel by a commonplace rubber ball as in Moschen’s act because the ball’s path has been (approximately) reversed. It now travels back to the floor, where its tendency to move rightward and the clockwise rotation set up another frictional force, this time to the right.

This force sends the ball off the right, almost along its initial path and thus back to the hand of the person who threw it down. A normal elastic ball would never return to the thrower.

Moschen makes use of this strange Super Ball behavior in one of his acts where he juggles balls that bounce underneath a horizontal metal surface:

Moschen’s web site is here

Other Super Ball tricks and surprises can be found in The Flying Circus of Physics book in item 1.76, and a few of the tricks can be seen in the following videos. I’ve also include here two other acts based on the classic Moschen act. trick orthogonal separated slanted

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Strobel, G. L., "Matrices and Superballs," American Journal of Physics, 36, 834-837 (1968)
··· Garwin, R. L., "Kinematics of an ultraelastic rough ball," American Journal of Physics, 37, 88-92 (1969); reprinted in The Physics of Sports, Volume One, A. Armenti Jr., editor, American Institute of Physics, 1992, ISBN 0-88318-946-1, pages 81-85
· Johnston, G. T., "The scientific method and the cooled Superball," Physics Teacher, 16, 172-173 (1978)
·· Crawford, F. S., "Superball and time-reversal invariance," American Journal of Physics, 50, 856 (1982)
·· Johnson, K. L., "The bounce of 'Superball'," The International Journal of Mechanical Engineering Education, 11, 57-63 (1983)
· Walker, J., "Success in racquetball is enhanced by knowing the physics of the collision of ball with wall" in "The Amateur Scientist," Scientific American, 251, 215-227 + 230 (September 1984); reprinted with added notes in J. Walker, Roundabout: The Physics of Rotation in the Everyday World, Freeman, 1985, pages 8-12
·· Bridges, R., "The spin of a bouncing 'Superball'," Physics Education, 26, 350-354 (1991)
· Doherty, P., "That's the way the ball bounces," The Exploratorium Quarterly, 15, 20-24 (fall 1991)
··· Barger, V., and M. Olsson, Classical Mechanics: A Modern Perspective, second edition, McGraw-Hill, 1995, pages 214-219
··· Cross, R., “Measurements of the horizontal coefficient of restitution for a Superball and a tennis ball,” American Journal of Physics, 70, No. 5, 482-489 (May 2002)
··· Cross, R., “Grip-slip behavior of a bouncing ball,” American Journal of Physics, 70, No. 11, 1093-1102 (November 2002)
··· Hefner, B. T., “The kinematics of a Superball bouncing between two vertical surfaces,” American Journal of Physics, 72, No. 7, 875-883 (July 2004)
··· Domenech, A., “A classical experiment revisited: the bounce of balls and Superballs in three dimensions,” American Journal of Physics, 73, No. 1, 28-36 (January 2005)
· Clark, R. B., “That’s the way the bouncing ball spins,” Physics Teacher, 44, 550 (November 2006)
··· Tavares, J. M., “The elastic bounces of a sphere between two parallel walls,” American Journal of Physics, 75, No. 8, 690-695 (August 2007)
··· Aston, P. J., and R. Shail, “The dynamics of a bouncing spuerball with spin,” Dynamical Systems, 22, No. 3, 291-322 (September 2007)
·· Knipp, P., “Bouncing balls that spin,” Physics Teacher, 46, 95-96 (February 2008)

1.77  Bounce of the ball
Jearl Walker
November 2007 
 Yesterday the Cleveland Browns won their (American) football game with the arch rival Baltimore Ravens by first tying the game with a field goal kick. That last-second kick was for a remarkable distance of 51 yards, but initially the kick seemed to have failed because the football hit one of the uprights on the goal and apparently then bounced back toward the players. To score, the ball must pass through the vertical plane formed by the two uprights, and so a bounce back toward the players would not count.

However, as you can see in the video game version of the kick at 

the ball actually hit the upright, passed through the vertical plane of the two uprights (thus scoring points), hit the horizontal support bar behind the uprights, and then bounced back over the crossbar and toward the players. The other team was so convinced that the kick had failed, that they left the field, only to be called back after the referees gathered to discuss the kick and then ruled that it was good. Those points tied the game and sent it into overtime, in which the Browns made another successful field goal kick and won.

Anyone can say that the bounce back over the crossbar was just freaky, because we normally expect that a ball that hits the upright and then the horizontal support bar should continue to move away from the players. What could cause it to bounce back toward the players?

Here is the physics (and notice that physics can answer the question whereas sports radio is just filled up with guesses and speculations or, if you are a fan of the Browns, tales of divine intervention). The collision of the ball with the upright gave the ball a lot of spin. Although the motion was complicated, the general direction of the spin was that the bottom of the ball rotated away from the players (the ball had backspin).

When the ball hit the horizontal support post, the spin tended to slide the ball’s bottom surface along the post, away from the players, but because the ball hit hard, it flattened on the post and could not slide. The resulting friction force on the ball from the post opposed the sliding and thus was directed back toward the players. So, when the ball recovered from the impact and began to bounce away, the friction force launched it back toward the players, sending it over the crossbar.

“Physics is everywhere” and is even in a Browns-Ravens football game.


1.78  Nike football commercial: real or fake?
Jearl Walker
Nov 2007
Controversy rages across sports blogs and video sites about a Nike commercial starring the famous footballer Ronaldinho, who performs four stunning shots at a goal. With each of the quick, successive shots, the ball bounces high from the crossbar on the goal and returns to Ronaldinho, who fields it and makes the next shot. Is the video real or fake? Here is the link for you to decide. Wait until he starts shooting the ball toward the goal

If you search through the posted comments about the video, you’ll find several arguments about why the video must be fake. Some people argue that the ball control is just unbelievably good and thus cannot be real. Other people argue that slow-motion analysis reveals some inconsistencies in the video, such as the ball briefly disappearing or the background abruptly changing. Other people staunchly defend the video as being real, dismissing the doubters.

All this stuff consists of little more than opinions. The power of physics is that you can cut through opinions to get at the truth.

Here is what I see in the video. Ronaldinho kicks the ball below its center so as to send it upward to hit the crossbar. Kicking low on the ball creates backspin. That is, the top rotates back toward Ronaldinho (hence backspin) and the bottom rotates away from him. When the rotating ball hits the crossbar, a friction force acts on the ball at the point of contact. Because the front of the ball is rotating upward, the friction force acts downward on the ball, opposing the tendency of the ball’s surface to slide upward across the crossbar. Although the friction force is very brief, it is enough to flatten the rebound path, perhaps even noticeably sending the ball downward.

Racquetball players know this result well. When a player wants the ball to rebound high, the player strokes the ball somewhat across the top to give the ball topspin. Then the friction force on the ball during the collision with the wall is upward, sending the ball upward. With backspin and a downward friction force, the ball leaves the wall headed downward toward the floor. Racquetball players use topspin and backspin to confuse an opponent about the direction a rebounding ball will take.

What do we see in the football video? With each shot, the ball rebounds high (in fact, impressively high), not downward. So, sorry, I just don’t believe the video. What do you think?

What good is physics? Physics can keep you from being fooled.

· · Griffing, D. F., The Dynamics of Sports: Why That's the Way the Ball Bounces, Dalog Co., 1982 (P. O. Box 243, Oxford, Ohio, USA 45056), pages 166 ff
· · · Andrews, J. G., "A mechanical analysis of a special class of rebound phenomena," Medicine and Science in Sports and Exercise, 15, No. 3, 256-266 (1983)
· Walker, J., "Success in racquetball is enhanced by knowing the physics of the collision of ball with wall" in "The Amateur Scientist," Scientific American, 251, 215-227 + 230 (September 1984); reprinted with added notes in J. Walker, Roundabout: The Physics of Rotation in the Everyday World, Freeman, 1985, pages 8-12
· · Bridge, N. J., “The way balls really bounce,” Physics Education, 33, No. 4, 236- (July 1998)
· · · Cross, R., “Grip-slip behavior of a bouncing ball,” American Journal of Physics, 70, No. 11, 1093-1102 (November 2002)
· · · Cross, R., “Bounce of a spinning ball near normal incidence,” American Journal of Physics, 73, No. 10, 914-920 (October 2005)

Want more references? Use the link at the top of this page.

1.81  Robbie Maddison’s motorcycle jump
Jearl Walker
April 2009   Here is, arguably, the most impressive motorcycle jump ever made --- Robbie Maddison roared off a ramp at 80 kilometers per hour and landed on top of a replica of the Arc de Triomphe, 37 meters above ground level. And then he drove off one edge and freely fell until he slammed into a descent ramp. The danger was fascinating but something else caught my subconscious attention, something that required me to watch the video a dozen times before I understood what I was seeing.

Here are several links to the video.

When an object is rotating, we can describe the “amount” of its rotation with a property called angular momentum, which depends on how fast the object is rotating and how its mass is distributed around the rotation axis. It is not something for which you will have an intuitive feel, although it is behind the magic of an ice skater’s spin and a ballet performer’s tour jete.

Here is the big point.

The angular momentum of an object (this measure of the rotation) can change only if a torque (due to a force) acts on the object.

Although the ideas of torque and angular momentum are abstract, you have playground experience with them. For example, if you push on a stationary merry-go-round at its center, you cannot make the merry-go-round rotate because the torque associated with such a push is zero. The angular momentum of the merry-go-round remains zero.

However, if you push along the rim, you are applying a torque to the merry-go-round, making it rotate and increasing its angular momentum. If you then push along the rim in the opposite direction, your torque causes the angular momentum to decrease, and so the merry-go-round slows and stops.

Let’s consider Robbie Maddison and his motorcycle as a single object and consider the torques acting on it when it is airborne. When the Maddison-motorcycle object left the ramp, it had a certain amount of angular momentum because of the rotation of the wheels.
If we make the reasonable assumption that the air drag did not produce an appreciable torque on the object, then we must conclude that the angular momentum of the object did not change during the flight to the top of the replica. However, in the video we see that the motorcycle rotated around a horizontal axis so that it landed on its front wheel rather than its rear wheel.

Such a landing was probably essential to Maddison’s safety because landing on the rear wheel and then having the front wheel slam down on the landing platform could have caused him to crash.

But how could the motorcycle rotate in midair to a nose-down orientation? Where did the angular momentum of that rotation come from?

The gravitational force cannot provide the angular momentum because that force acts through the center of mass of the Maddison-motorcycle object. Thus, that force is like your push on the center of the merry-go-round ---- it will not cause the Maddison-motorcycle object to rotate during the flight.

When I first watched the video of the flight, I subconsciously knew that something was strange but only after watching it a dozen times did I pinpoint the rotation as being the mystery. Only then did I realize that Maddison controlled the angular momentum --- as he flew through the air, he applied the brakes to the wheels, decreasing their angular momentum. Because the angular momentum of the Maddison-motorcycle object could not change, the motorcycle itself had to rotate in order to maintain the total amount of angular momentum. Maddison very cleverly transferred rotation from the wheels to the motorcycle itself.

If, instead, Maddison had gunned the engine and dramatically increased the angular momentum of the wheels, the motorcycle would have rotated in the opposite direction, that is, nose up. Landing with the motorcycle vertical or upside down would have been disastrous.

To see the difference between applying the brakes and gunning the engine, note that in the video the wheels rotate clockwise in our view and thus have a certain amount of clockwise angular momentum when the motorcycle leaves the ramp. By slowing the wheels with the brake, the motorcycle must then rotate clockwise (bringing the nose down) in order to maintain the same total amount of clockwise angular momentum. If Maddison had gunned the engine and increased the clockwise angular momentum, the motorcycle would have had to rotate counterclockwise to offset that increase.

Some motorcycle performers bear down or pull up just as the motorcycle is leaving a ramp. Such action may have a small effect on the flight. The performer may also move away from the normal sitting position during the flight in order to affect the motorcycle’s orientation. This is certainly used by performers in X games in which a performer might almost completely lose contact with the motorcycle in midair, but I cannot see that Maddison used any technique like this.

When Maddison drives his motorcycle over the edge of the replica and free falls, the Maddison-motorcycle object again rotates to a nose-down orientation so that the motorcycle can land on both wheels almost simultaneously on the descent ramp. However, this time Maddison did not control the rotation. When he leaves the edge, the wheels are rotating only slowly. Even if he applies the brakes, there is little angular momentum to be transferred from the wheels to the motorcycle itself.

This time, the nose-down rotation was due to the way the motorcycle left the replica. As the front wheel went over the edge, the front of the motorcycle began to fall, producing a rotation around the support point under the back tire. In this case, the gravitational force does change the angular momentum because it pulls the front end of the motorcycle down while the rear end is still supported.

Once the rear wheel went over the edge, the Maddison-motorcycle object had a certain amount of angular momentum, which did not change until the motorcycle hit the ramp. The rotation was not fast but was enough to bring the motorcycle into proper orientation. Although Maddison was well experienced in rotating the motorcycle by using the brakes during a jump, he had no experience with the rotation during such a long fall. He and his staff must have done calculations on the extent of rotation as a function of the distance of falling, and then they must have adjusted the height and slope of the landing point on the descent ramp.

There is nothing better than the possibility of death to sharpen someone’s appreciation of careful physics. instructions part 1 of a longer broadcast part 2 distance jump. You can see the bike orientation change.

Want more links? Go to this pdf file and scroll down to item 1.81.

1.81 Car jumps
Jearl Walker
March 2013 Here is a car jump that almost ends in a crash. The car comes down from a high ramp and onto the launch ramp, and it then flies through the air to the landing ramp.

As the narrator explains, the car had too much speed as it was launched and thus nose-dived into the landing portion. Here is shot with the car in flight and another shot taken along the landing ramp.

But wait. Too much launch speed could cause the car to overshoot the landing ramp, but what has the speed got to do with the orientation of the car as it lands?

The center of mass of the car flies through the air pretty much like a baseball does: It follows a parabolic path set by the downward gravitational force and the launch speed and angle. For a set launch ramp, a greater speed results in a longer range to the landing point. Thus, before a car is jumped, someone must figure out, either through calculations or (better) experimentation, where to place the landing ramp. Because air drag shortens the range somewhat and can vary from jump to jump, the ramp is made long enough to allow for the variation.

The orientation of the car should be set by the launch angle, because the car comes straight off the launch ramp. If the ramp is set at, say, 30 degrees to the horizontal, the car’s launch orientation is also 30 degrees and that should not change during the flight. Thus, the car should land tail first, still at the same orientation. Here is a video in which the car’s orientation does not change as much during the flight as we see in the first video. Ken Block jumps 171 feet

In the first video the car noticeably changes its orientation so that it nose dives into the landing ramp and the driver momentarily loses control. As the narrator points out, if the car support structure had not been strengthened, the car would have crashed.

So, why did the car’s orientation change during flight so that it nose-dived? The cause is rather subtle because it has to do with the angular momentum of the wheels and the car as a whole. In our view of the car, the wheels are rotating counterclockwise. We assign a certain angular momentum to that rotation: it is the product of the rotation speed and the distribution of mass around the rotation axis of each wheel. When the car leaves the ramp, it has a certain total amount of counterclockwise angular momentum.

Once the car is in free flight through the air, with only gravity and air drag acting on it, that total amount cannot change because there is no force to set up a torque to change it. Gravity effectively acts through the center of mass and cannot produce a torque. If the air drag on the underside is uneven, it might produce a torque but the effect would be small for the car’s quick flight through the air.

The secret in reorienting the car in flight lies in what the driver is doing during and just after the launch. If the driver holds the car speed constant during the launch, the car maintains its orientation during the flight. If the car speed is increasing during the launch, the front of the car rotates upward during the flight. And if the car speed is decreasing during the launch, the front rotates downward.

Let’s consider the situation when the speed is increasing. That means that the wheel speed is increasing just as the car is launched. And that means that the counterclockwise angular momentum of the wheels is also increasing. But in flight, the total angular momentum of the car cannot change. If the counterclockwise angular momentum of the wheels is increasing, that means that the car as a whole must begin rotating clockwise in order to maintain the same total angular momentum. Thus, in our view, the car rotates clockwise, which brings the nose up. The same thing happens if the driver guns the engine during flight.

Just the opposite happens if the car is decelerating at the launch or if the driver applies the brakes during the flight. Then the counterclockwise angular momentum of the wheels is decreasing and the car must rotate counterclockwise to maintain the total amount of angular momentum.

As Ken Block says in the second video, he can make the jump because he knows the physics. Of course, the jump also takes a bit of courage, including physics courage. lots of crashes

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
·· Brearley, M. N., "Motorcycle long jump," Mathematical Gazette, 65, 167-171 (1981)

1.84  Hula hoop
Jearl Walker
November 2014   How do you keep a hula hoop (the plastic ring under a trademark by Wham-O, Inc.) up and spinning around the body in an almost horizontal plane?

Once you send the hoop spinning around your midsection, you drive its motion by moving your body in circular motion. The contact point is continuously slightly ahead in the circling from the hoop, so the contact point pushes on the hoop. The continual pushing and spinning lifts the hoop in its normally horizontal orientation.

In this first video we see Masha Terentieva in an artistic performance with the Cirque du Soleil. Initially she spins a single hoop in many different ways, with torso, arm, or leg. Then she switches to two hoops which become mesmerizing. She ends with four hoops spinning in different planes: one on each arm, one a backward extended leg, and one on the vertical leg. Notice how at one point she has adjacent hoops spinning around her torso and then she is able to separate them upward one at a time by slightly tilting her torso.

Here next is the Guinness record for hoop spinning: Aleysa Gulevich managed (briefly) to spin an astounding 107 hoops. One of the difficulties is that she needed to move all 107 points of contact in approximately the same circular path.

Fans of hula hooping can catalog the various moves and patterns that are available in a performance. This next video goes through the list.

This next example is certainly not as pretty as the others, and certainly not dance-like. Here a man spins a heavy truck tire that he can barely lift.

But once he gets the tire spinning, the rotational motion brings the tire up to almost a horizontal orientation. (I bet his midsection was sore the next day. Indeed, in the medical literature several papers refer to a hula-hoop syndrome.)

Let’s end with another graceful and mesmerizing dance performance:

In the paper by Belyakov and Seyranian, theoretical work on hula hoop motion reveals that a reverse rotation is possible; that is, a clockwise rotation of the body can produce a counterclockwise rotation of the hoop, or vice-versa. So far I have not seen a video example.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
··· Caughey, T. K., "Hula-hoop: an example of heteroparametric excitation," American Journal of Physics, 28, 104-109 (1960)
··· Balasubramanianm, R., and M. T. Turvey, “Coordination modes in the multisegmental dynamics of hula hooping,” Biological Cybernetics, 90, 176-190 (2004)
·· Cluff, R., D. G. E. Robertson, and R. Balasubramaniam, “Kinetics of hula hooping: An inverse dynamics analysis,” Human Movement Science, 27, 622-635 (2008)
··· Belyakov, A. O, and A. P. Seyranian, “The hula-hoop problem,” Doklady Physics, 55, 99-104 (2010)
··· Seyranian, A. P., and A. O. Belyakov, “How to twirl a hula hoop,” American Journal of Physics, 79, No. 7, 712-715 (July 2011)


1.85  Yo-yos, unusual and gigantic
Jearl Walker
November 2012 Suppose that you drop a yo-yo rather than throw it downward. Normally when you drop an object, its potential energy is transformed into kinetic energy and the object travels progressively faster with descent. A yo-yo is different for two reasons: It rotates and the rotation rate depends on the thickness of the layer of wound-up string on the yo-yos shaft. As the yo-yo descends and unwraps that string layer turn by turn, the yo-yo spins faster and faster. That leaves less energy for the descent itself. As a result, the rate at which the yo-yo descends first increases and then, about halfway down, it decreases. When the yo-yo reaches the end of its descent and the string is completely unwound, the yo-yo bounces.

If the string is attached to the shaft (usually through a hole in the shaft), the yo-yo immediately begins to wrap back up on the shaft, with the direction of the yo-yo’s rotation unchanged. If, instead, the string is looped around the shaft and the bounce is not severe, the yo-yo will sleep. You can awaken it by jerking upward on the string. The jerk yanks the yo-yo upward and momentarily relieves the tension in the string. Since the yo-yo is turning, it catches up some of the slack string on the shaft. Provided there is enough friction, the captured section of string holds, and then the yo-yo is forced to wrap up more string, which makes it climb. If you wait too long to awaken a sleeping yo-yo, too much energy is lost to the rubbing between the shaft and the loop around it, and the yo-yo will be unable to climb back to your hand.

Well, that is the story for a normal yo-yo. Here is a video showing some large yo-yos that were designed for a contest.

And here is a video showing a gigantic yo-yo, large enough that if it fell on you, you would be killed. Yes, that would be sad but it surely would produce a hilarious obituary.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

·· Kofsky, I. L., "Yo-yo technics in teaching kinematics," American Journal of Physics, 19, 126-127 (1951)
·· Sommerfeld, A., Mechanics, Academic Press, 1964, pages 246-247
··· Burger, W., "Elementary dynamics of simple mechanical toys," Mitteilungen der Gesellschaft fur Angewandte Mathematik und Mechanik, 2, 21-60 (1980)
··· Burger, W., "The yo-yo: a toy flywheel," American Scientist, 72, 137-142 (1984)
· Harding, R., and R. Prigo, "The yo-yo top," Physics Teacher, 22, 36-37 (1984)
· Allman, W. F., "Physics on a string," Science 84, 5, 92-93 (October 1984)
· Walker, J., "A homemade device for testing particle scattering; experiments in zero gravity" in "The Amateur Scientist," Scientific American, 254, 114-118 + 120 (February 1986)
· Allman, W. F., "Yo-yos: physics on a string," in Newton at the Bat: The Science in Sports, E. W. Schrier and W. F. Allman, eds., Charles Scribner's Sons, 1987, pages 193-197
· Crane, H. R., "Help for forgetful car owners and lazy yo-yo throwers," in "How Things Work," Physics Teacher, 26, 240-241 (1988)
·· Boudreau, W., "Cheap and simple yo-yos," Physics Teacher, 28, 92 (1990)
· Valenti, M., "Spinning link," Mechanical Engineering, 113, No. 8, 104 (August 1991)
·· Krupa, E., and W. Tanska-Krupa, “Newton’s second law and the physics of the yo-yo,” Physics Education, 32, No. 3, 185-187 (May 1997)
· Weiss, P., “Reinventing the yo-yo,” Science News, 165, No. 16, 250-252 (17 April 2004)


1.91  Pub trick --- balancing a coin on a folded paper edge
Jearl Walker
February 2008
   Hold a crisp (new) dollar bill upright in front of you so that the numbers are right side up. Fold the top half down onto the bottom half, and then crease the folded edge so that it both straight and sharp (the paper bends tightly around the fold). Stand the bill up on a table, with the folded edge horizontal and at the top and the splayed free edges on the table. Challenge a friend there in the bar (or the family recreational room) to balance a coin on the folded straight edge. Of course, your friend will laugh at you, saying “that’s impossible!” So, you respond with, “Well, I can easily do it. Why can’t you?”

Although in principle the coin can be balanced if its center of mass (the center of its mass distribution) is placed directly above the folded straight edge, finding that precise positioning and then releasing the coin without disturbing it is almost impossible. If the center of mass is even slightly to one side of the edge, the gravitational pull on that side of the coin exceeds the pull on the other side, and, like an unbalanced see-saw, the coin rotates around the edge. And the coin is also sure to rotate off the bill if your release gives it even a slight rotation.

Of course, if the support were wider, positioning the coin would be easier, but that is why you sharply crease the bill before you challenge your friend.

After your friend gives up, you balance the coin on one try and can even lift the bill without spilling the coin. Here is the secret: As shown in the video from, ,

you add another fold to the bill by folding the right side onto the left side. Sharply crease the new fold and then set the bill down on its splayed free edges so that it forms a V as seen from above. With a bit of care, position the coin with its center approximately above the apex (point) of the V. Then, pull the ends of the V in opposite directions so as to straighten out the V until the original fold is again straight. If you have steady hands, you can even lift the bill without spilling the coin.

That much is shown in the video, but the real challenge here is to explain why the trick works. Stability is very difficult to achieve if you attempt to balance something on one or two points. On one point, a chance disturbance (such as your release) can easily rotate the object’s center of mass so that it is no longer exactly above the support point, and so the gravitational force continues the rotation.

The situation is hardly better with two support points, as someone might have if walking along a stretched high-wire in a circus act. Although the object is relatively stable parallel to the line connecting the support points, it is unstable against any chance motion perpendicular to the line. This instability is not improved if there are many support points along the line, which is the situation you initially have with the dollar bill folded only once.

However, if the object is supported by three points that do not form a straight line, then it might be stable. And that is exactly what you set up if you make a second fold on the dollar bill. In fact, you have many points of support that form a V under the coin. As long as the coin’s center of mass lies above the region anywhere within the V, it is relatively stable.

When you pull the bill to straighten out the folded edge, the sharply creased second fold maintains its shape and thus the bill still forms a V below the coin. Although the V is now smaller, the coin is still stable is its center of mass lies above the region within the V. Because the V is hidden below the coin, the person you challenged cannot see it and thus can only marvel at your ability to balance the coin after you have apparently straightened out the bill.

1.92  Bull riding
Jearl Walker
January 2015  The motto of the FCP book and this web site is that physics is everywhere. Here is an example that maybe you never considered: the physics of bull riding, in which a rodeo cowboy needs to ride a bull by hanging on to a harness with one hand. The bull, of course, resents the rider on its back and thus jumps and spins to throw the rider off.

You can see the action in this video:

The rider’s perch depends on the location of the bull beneath him, but the bull suddenly twists, pitches, runs, and stops. With each sudden move of the bull, the rider’s momentum and angular momentum tend to send or rotate him from his perch. If he just holds on to the strap with both hands, he must use his strength to arrest the motion of the upper portion of his body off his perch.

He can do better if he throws one arm high while holding on to the strap with the hand of the other arm. He can then throw the free arm in a direction that counters any sudden rotation given him by the bull. The free arm must be held high instead of low so that its mass is far from the center about which the rider tends to rotate at any given instant. Only then can the motion of the free arm effectively counter the rotation of the more massive upper body. If the rider holds a large hat with the free hand, the air drag on the hat as it is waved might give an extra measure of resistance to the rotation of the upper body.

Additional physics is explained in this next video (very cute but turn up your volume):

Some bars, especially in regions where rodeos are popular, have mechanical bulls for customers to ride. Here is a video where a person sets the Guinness World Record for mechanical bull riding.

I may understand the physics behind bull riding, but I would not last even as long as the woman does toward the end of the video.


Dots · through ··· indicate level of difficulty

Journal reference style: author, title, journal, volume, pages (date)

Book reference style: author, title, publisher, date, pages

· Brancazio, P. J., Sport Science: Physical Laws and Optimum Performance, Simon and Schuster, 1984, ISBN 0-671-45584-2, pages 144-147

· Thomson, K. S., “Marginalia,” American Scientist, 75, No. 1, 69-71 (January-February 1987)

1.94  The dambusters of World War II
Jearl Walker
June 2008   Last month marked the 65th anniversary of the Allied attack on the German dams in the Ruhr, using a very unconventional weapon---a rotating bomb that skipped over the water and then rolled down the dam face to explode at a predetermined depth next to the base of the dam. The inventor was Barnes Wallis, an aeronautical engineer who designed the British R100 airship in the 1920s.

Through calculation and experimentation, he realized that the massive dams, which were vital to the German war effort, could not be breached by standard bombing. Indeed, if only one bomb were used, the bomb would have been so large that the airplane could not have taken off and carried it from England to Germany. Wallis and the RAF also knew that torpedoes could not be used against the dams because torpedo nets were stretched across the lakes to catch any torpedo dropped by an attacking airplane.

Wallis soon hit upon the idea of dropping a rapidly rotating bomb that would skip over the water like a stone thrown by a child, skipping over the nets and smacking against the dam wall. Although Wallis first considered a spinning spherical bomb, he eventually settled on a cylindrical bomb that would be given a backspin of about 500 revolutions per minute in the airplane prior to release. The rotation was set up by a system of sprockets and chains (somewhat like on a motorcycle) that was driven by the main hydraulic system of the airplane.

Here are the three points of Wallis’s argument for using rotation and backspin:

1. The rotation stabilized the cylinder during the fall and then during the skipping flight to the dam, much as rotation stabilizes a gyroscope.

2. Because of the backspin, the bottom surface rotated toward the dam and thus moved in the same direction as the bomb as a whole. That meant that the surface was moving at high speed when it hit the water, driving up a ridge of water in front of the point of impact. The bomb bounced upward and forward from that ridge. Although water is certainly fluid, when it is hit rapidly, it is almost rigid, a feature that you may have noticed if you have ever “belly-flopped” (belly first) or “cannon-balled” (rear end first) from a high diving platform into a pool of water.

3. When the bomb hit the dam wall, it was still rotating and thus rolled down the wall to the base of the wall, which is where it was designed to explode. If the bomb had exploded at the water surface, it might have broken some of the wall but perhaps only a small of amount of water would have been lost through such a break at the top. However, if the bomb cracked the wall at the bottom, the very high water pressure there would blow the wall apart. That was Wallis’s plan --- one or two carefully placed bombs could destroy what hundreds of larger bombs dropped directly on the dam could not destroy.

On May 17, 1943, three groups of Lancaster bombers left England for the attack, flying in moonlight just barely above the water in the English Channel and then barely above the trees over the land, hoping to avoid German radar. When the bombers reached a dam, not only did they have to attack the dam in only moonlight, they had to release each spinning bomb at a predetermined height and distance from the dam. The height was short, about 18 meters, or otherwise the impact would burst the bomb package. At that time, airplanes did not have altitude sensors that could measure such a short height. So, the RAF devised a surprisingly simple scheme. A spotlight was mounted under the front of the airplane and another was mounted under the belly, and the two beams were angled such that when the airplane was at the correct height, the two spots of light on the water overlapped.

The attack on the dams is depicted well in the 1954 movie The Dambusters, based on the 1951 book The Dam Busters by P. Brickhill. Below here I’ve listed several links to clips from the movie. I recommend that you watch at least the video about the attack on the first dam, the Moehne, to get a feel for the conditions. The first bomb rolled down the dam just right but failed to break it apart. The second bomb overshot the dam and exploded when it landed on the power station on the opposite side. The third bomb hit exactly right but seemingly failed to break the dam. As the next airplane made its run at the dam, the dam suddenly broke apart. Wallis was exactly right --- the shock waves from one or two bombs at the base of the dam was enough to rupture the concrete and allow the high water pressure at the base to blow out the dam.

The dams destroyed by the spinning, skipping bombs that night seriously damaged the German war effort. The attacks also resulted in significant numbers of artillery units being moved from the frontlines to the remaining dams. However, for countless people on both side of the war, the intriguing aspect of the dambusters is how the physics of a child’s game of skipping rocks could be employed in destroying massive concrete constructions.

Some of the links here take you to the movie’s version of the attack on the second dam and several old documentaries about the dambusters and their bombs, including the experiments with spherical bombs. There are also links to some original footage of the German tests with skipping bombs---they were rocket propelled as they dropped away from the airplane. (Presumably the tests were not continued because the German V-2 rockets that were bombarding England were so successful.) I’ve also included links to video about the anniversary ceremonies that were held last month. The photo here (from d1ngy_skipper) shows a Lancaster bomber at the ceremonies. 1954 movie The Dambusters. Here is the part about the attack on the first dam. Here is the part of the 1954 movie that shows the attack on the second dam documentary The German version of the bouncing bomb The German version

Dmbusters anniversary in May 2008 video news item about the anniversary, with a Lancaster airplane flying by video from the cockpit of the Lancaster airplane during anniversary flyby News item about the dambusters Dambusters web site

· Brickhill, P., The Dam Busters, Evans Brothers, London, 1951
· Stinner, A., "Physics and the dambusters," Physics Education, 24, 260-267 (1989)

1.94  Stone skipping on water
Jearl Walker
June 2006   Recent experiments and wonderful high-speed photos reveal the mechanics of a stone skipping over water. The stone, actually an aluminum disk, was launched by a catapult device that could control both launch speed and rotation rate. The researchers discovered (or rediscovered) that if a stone is to skip, its speed must exceed a certain threshold value or the stone merely skims (surfs) over the water top for a short distance before stopping and sinking. The stone’s rotational speed must also exceed a certain threshold value. The spinning stabilizes the stone much like spinning stabilizes a gyroscope. Then the stone maintains the same orientation (with the front end tilted upward by 10º to 20º from the water surface) for its entire skipping path. From skip to skip, its horizontal speed is almost constant, but its vertical speed (due to its being thrown upward by each crash into the water) decreases, until finally the stone just skims. A video of Kurt Steiner setting the world’s record of 40 skips can be seen at on the Web. 

· · ·  Bocquet, L., “The physics of stone skipping,” American Journal of Physics, 71, No. 2, 150-155 (February 2003)
·  Dume, B., “How do stones skip?” Physics World, 16, ?? (January 2003)
· ·  Clanet, C., F. Hersen, and L. Bocquet, “Secrets of successful stone-skipping,” Nature, 427, No. 6969, 29 (1 January 2004)
· · ·  Nagahiro, S., and Y. Hayakawa, “Theoretical and numerical approach to “magic angle” of stone skipping,” Physical Review Letters, 94, article # 174501 (4 pages) (6 May 2005)
· · ·  Rosellini, L., F. Hersen, C. Clanet, and L. Bocquet, “Skipping stones,” Journal of Fluid Mechanics, 543, 137-146 (2005)
·  Bocquet, L., and C. Clanet, “The mystery of the skipping stone,” Physics World, 19, No. 2, 29-31 + front cover (February 2006)

Want more references? Use the link at the top of this page.

1.94  Golf ball skipping over water
Jearl Walker
January 2012 In the video, a golfer hits the ball almost directly into a water trap. The ball then skips several times over the length of the water trap and bounds up onto the green and rolls around until it finds the cup.

The shot was deliberate of course, because normally the ball would be lofted over the water and onto the green. But why didn’t it simply sink as golf balls commonly do when landing in water traps?

A ball is lost in a water trap if it rolls off the bank and into the water. There it sinks because it is denser than water, and thus the buoyancy acting upward on it is insufficient to counter the gravitational force acting downward on it. A ball is lost if it hits the water at a fairly large angle to the water surface, as occurs at the end of a long, high flight. Although water is fluid, it can be almost rigid if hit at high speed. (That rigidity is the fatal factor if someone jumps from a high elevation into water, as tragically happens at some bridges.) When the ball hits, it stops and then sinks.

However, if the ball hits at a shallow angle and at high speed, as we see in the video, it can bounce from the water, maintaining most of its forward momentum. If you step through the video you’ll see a small splash of water at the site of the first impact, revealing that water was not perfectly rigid.

The other feature of the golfer’s shot is that he put a large top spin on the ball by hitting it above the ball’s center of mass. That is, as the ball flew off the tee, its top surface rotated away from the golfer and the bottom surface rotated toward the golfer. This rapid spin stabilized the golf ball by giving it a large angular momentum.

We can tell that the ball had a large top spin by the way it moved on the green: it rolled rapidly in the forward direction. If a golfer puts backspin on the ball, then the ball tends to either stop or roll backward when it lands on the green.

The shot in the video appears to be a deliberate demonstration of getting the ball to skip over the water. In this next video, several golfers have transformed such skipping into a contest. Well, I guess if you loved skipping stones as a youngster and grew up to love golf, this is a natural outcome.

1.97  Cats turning over to land in a fall
Jearl Walker
Sep 2008 
   If a cat falls out of, say, a tree, it somehow knows how to rotate itself to land feet first, so that its legs can act as shock absorbers. In that way, the cat takes longer to come to a stop, which means that its acceleration (which could be harmful or even lethal) while stopping might be only moderate. Here are two links to the same video (but one with slow motion) showing a cat as it falls from a tree. skip the commercial at the start. 80 ft fall. Watch the tail. Here is the same fall but with footage after the fall to show that the cat is (probably) ok.

The landing is understood but the rotation process has been controversial for centuries. In The Flying Circus of Physics book I outline the two main arguments. One of them involves the tail: The cat quickly pulls in its front legs and then whips its tail around counterclockwise. Because the cat is isolated from any torque (there is no outside force to cause it to rotate), the counterclockwise motion of the tail must be balanced by a clockwise motion of the rest of the body. We attribute this need of balance to the conservation of angular momentum. Angular momentum is a measure of the rate of rotation and the distribution of mass around the axis of rotation. The point here is that, with no outside torque to change the rotation, the rotation of part of the cat must be balanced by the rotation of the rest of the cat in the opposite direction.

Because the front legs are pulled in, the front half of the body is easier to rotate and thus rotates a bit farther than the rear half. Of course, this leaves the cat somewhat twisted. So, it then pulls in its rear legs and extends its front legs. Now the rear half rotates more than the front half. By now the cat should be approximately in a feet-down orientation so that it can land.

Cats usually do not take physics courses, but they have an intuitive feel for at least this much physics. You and I don’t have that much --- if we fell out of a tall tree, we would just wildly wave our arms and legs. A cat on the ground would surely laugh at our antics. Well, cats are actually way too smug to laugh, but they would at least inwardly grin.

· "Photographs of a Tumbling Cat," Nature, 51, 80-81 (1894)
· McDonald, D. A., "The righting movements of a freely falling cat (filmed at 1500 f.p.s.," Journal of Physiology, 129, 34P-35P (1955): special pages devoted to Proceedings of the Physiological Society for 15-16 July 1955
· · ·  Routh, E. J., Dynamics of a System of Rigid Bodies, Part 1, Dover, 1960, page 238
·  McDonald, D. A., "How does a cat fall on its feet?" New Scientist, 7, 1647-1649 (1960)
·  McDonald, D. A., "How does a man twist in the air?" New Scientist, 10, 501-503 (1961)
· · ·  Kane, T. R., and M. P. Scher, "A dynamical explanation of the falling cat phenomenon," International Journal of Solids and Structures, 5, 663-670 (1969)
· · · 
Essen, H., "The cat landing on its feet revisited or angular momentum conservation and torque-free rotations of nonrigid mechanical systems," American Journal of Physics, 49, No. 8, 756-758 (August 1981)
· Cooke, P., "Acrobatics: physics with a twist," Science 84, 5, 86-87 (June 1984)
· Darius, J., “The tale of a falling cat,” Nature, 308, No. 5955 (8 March 1984)
· · Edwards, M. H., "Zero angular momentum turns," American Journal of Physics, 54, 846-847 (1986)
· Laws, K., "Comment on 'Zero angular momentum turns'," American Journal of Physics, 56, 81 (1988)
· Edwards, M. H., "Reply to 'Comment on zero angular momentum turns'," American Journal of Physics, 56, 81-82 (1988)
·  Fredrickson, J. E., "The tail-less cat in free fall," Physics Teacher, 27, 620-625 (1989)
·  Galli, J. R., “Angular momentum conservation and the cat twist,” Physics Teacher, 33, 404-406 (September 1995)
Want more references? Go to the reference list for Chapter 1 of The Flying Circus of Physics book
and then scroll down to item 1.97

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