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Flying circus of physics

Chap 1 (motion) archived stories part E

Sunday, February 08, 2009



For Chapter 1, here is part E 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

http://www.flyingcircusofphysics.com/pdf/Chapter1_Ref_Com.pdf


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

--------- New items (not in the book):
1.200  Flea circus
1.201  Stacking stones and bowling balls

1.202  Cars on ice
1.202  Cars on ice -- the 2010 video collection
1.203  Penn and Teller magic, with Teller as possible road kill
1.204  Implosion demolition
1.204  Rolling a building down the street
1.204  Building topples over
1.205  Wheel of Death

1.206  Falling cranes --- from silly to deadly
1.207  Twining plants on a garden rod
1.208  Indiana Jones and the Kingdom of the Crystal Skull
1.209  Alligator death roll



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
 

1.200  Flea Circus
Jearl Walker www.flyingcircusofphysics.com
July 2007
When I was a first-year student at MIT, the most bizarre physics film I saw was called “A Million to One.” It was a grainy black-and-white “film loop” about a flea circus (in Times Square in New York City, I think). A wire harness connected a flea to a miniature cart, with tiny wheels. When given a poke by the “master,” the flea would struggle forward, pulling the cart. The flea was able to accelerate the cart, even though the ratio of the cart’s mass to the flea’s mass was huge (hence the name of the film). The fact is that the acceleration is due to the relatively strong force of the flea’s legs pushing against the table top, not the flea’s mass.

The film was more surrealistic than educational or even entertaining. Watching a flea pull a cart is not riveting cinema, but you should understand that I saw the film long before the invention of the internet and YouTube. Yet, it seems fitting that one of the videos currently on YouTube shows a modern version of a flea circus, completely with performing fleas that an onlooker must view through a microscope. When I came across the YouTube listing, my heart skipped a beat---was this really a flea circus, with a flea trained to pull a cart? I flashed back to first-year physics at MIT (not the most pleasant thing to do). I pulled up the YouTube video and yes! yes! There was a flea, straining to accelerate a much more massive cart! With strong legs and a good poke, the flea accelerated a relatively large mass.

Something similar is already described in The Flying Circus of Physics: with legs straining, someone pulls a train, which is many orders of magnitude larger in mass than the person. (You always have options in life. If you don’t want to learn math, well you can always pull trains. I guess it is better than holding up liquor stores with a gun.)

Since I was at MIT, the Beatles, Joy Division, the Clash, and the Clan of Xymox have all come and gone. But fleas pulling carts are still around, still offering a lesson in physics. I suppose I should find that comforting.

http://www.youtube.com/watch?v=A2ok83HKRI0 Watch the fleas pull carts with a weight much greater than their own.
http://www.youtube.com/watch?v=gauReGP_Tps&feature=related 

1.201  Stacking stones and bowling balls
Jearl Walker
www.flyingcircusofphysics.com
July 2007   In the past, men stood up stones such as those in the circles at Avebury and Stonehenge or stacked them such as those in the huge pyramids of Egypt. The “upright” and “stacking” urges are still around these days, but perhaps they are a bit more modest and urban. Many of the following links take you to videos and photos of upright and stacked stones, but let me counter the first thought that you’ll have when you see them. No, the stones are not glued together by some glue-head who has sniffed too much of the vapors. Instead, what you see are magnificent examples of balancing. In some of the videos, you get to see a balancer put one more stone on the top of a stack of stones. Watch how he searches for the correct position of the new stone.

A related balancing act can sometimes be seen in bowling alleys (the American type of bowling, sometimes called ten pins) when the manager is not looking (the stunt will get you thrown out). Bowling balls are stacked one on top the other to a height of five or more balls. The photo here, by busbeytheelder,  shows a stack of four balls.  

Now, how can either stone stacks or bowling-ball stacks be built? Why don’t the objects just fall off one another?

Let’s start with the bowling balls. In principle, you can balance a spherical ball on top of another spherical ball if you position the center of mass of the top ball directly above the contact point between the two balls. If the mass in the ball is uniformly distributed, the center of mass is located at the center, and so you want to align the center over the contact point.

However, this type of balance is known as unstable equilibrium because even the slightest disturbance ruins it by ruining the vertical alignment. Even the chance vibration from the floor due to someone’s footstep or the chance breeze from a room’s temperature control system is enough. Then, of course, the top ball rolls or slides off the top and onto the floor. No one is going to be impressed with that. Thus, balancing with one point of contact is not stable.

If you could arrange for the two balls to make contact along a straight line, they still would be unstable because the top ball could easily rotate around the line and fall. Thus, balancing with a straight line of contact is not stable.

However, a bowling ball is neither uniform nor perfectly spherical because it has finger holes, and you can balance one ball on top another one if you arrange for the contact to be at one of the finger holes of the top ball. Then contact is made along a small circle, the perimeter of the round finger hole. If the center of mass of the top ball is aligned over any point within the area of that circle, the ball is balanced. The balance is precarious in that it will not survive a sharp hit by your hand, but it is stable against normal floor vibrations.

However, stacking multiple bowling balls is challenging for two reasons. (1) The slight jostling required of positioning the top ball can easily move the center of mass of a lower ball off its alignment. (2) The slight misalignment of the center of mass of a ball from the central axis through the balls can eventually make the whole stack unstable. Here is a project: Is there a theoretical maximum height to a stack of bowling balls?

Stacking stones is very similar to stacking bowling balls: You need more than two points of contact and the center of mass of the higher stone must be aligned over the area between those contact points. As you can see in the videos, you can stack stones that radically differ in both shape and size.

Balancing bowling balls

http://www.youtube.com/watch?v=0Km-gXbSiDo   Video, almost gets seven
http://www.youtube.com/watch?v=BtQYxJvTRZ4&NR=1 Video, stack of six bowling balls
http://www.youtube.com/watch?v=mG_57Nfr16I Video, stack of five bowling balls

Sculpture of balanced rocks and pebbles
http://www.youtube.com/watch?v=1JkEpLdEJY8&mode=related&search= Video, audio is low but try to listen. Watch him balance a heavy rock.

http://www.youtube.com/watch?v=kKXWfaVj5sE&mode=related&search= Video of Bill Dan’s balanced rock sculptures

http://www.youtube.com/watch?v=C1rwBbKhs0M&mode=related&search= Video, watch him search for the balance

http://www.youtube.com/watch?v=Y9hDumXOgQM&mode=related&search= Video of balanced rock array.

http://www.youtube.com/watch?v=9ci-BecLfJI Video, in reverse

http://www.youtube.com/watch?v=RHMEWxZjvnI&mode=related&search= Video, discussion and an array of many sculptures

http://www.rock-on-rock-on.com/ Bill Dan’s gallery of photos (and a video): Rocks balanced on rocks. Stunning! No, they are not glued together. They are actually balanced. Use the button at the bottom and the menu at the right to click through many pages of photos.

http://www.teamsandtastic.com/RockStacking/ Photos, Team Sandtastic, Professional Rock Stacking and Rock Balancing

http://www.flickr.com/photos/dgbalancesrocks/sets/1572008/ Dave Gorman, photos, rock and pebble balancing

http://www.youtube.com/watch?v=EoWaxssQUU4 Video, shot glass balanced on a coin

http://www.terragalleria.com/pictures-subjects/balanced-rocks/ Terragalleria, photos by Q. T. Luong, natural precariously balanced rock and balanced rock art

http://www.urbanshamanism.com/CloseUpPages/BalancingRocksCU.html Photos of more balanced rocks

http://www1.flickr.com/photos/dgbalancesrocks/299241134/ Photos

http://www.neara.org/Moore/balancedrocks.htm Photos and discussion of naturally balanced rocks

http://gocalifornia.about.com/bl_utgsescphoto_bal.htm Photo

http://www4.flickr.com/photos/sovietuk/10490661/ Photo

Reference

· · · Macomber, H. K., “Equilibrium of tipping rocks,” American Journal of Physics, 51, No. 11, 1045-1046 (November 1983)



1.202  Cars on ice
Jearl Walker www.flyingcircusofphysics.com
July 2007 
Everyone can watch a car wreck and be either amused or horrified. The power of physics is that you can explain what happens. For example, consider car wrecks on ice, as shown in the videos at the following three URLs. Your ability to drive a car depends on the coefficient of friction between the tires and the road. As you already know, if the tires turn smoothly without slipping on the road, the car moves forward (or backward, if you want). But if the tires slip, you have little or no control over the motion of the car, regardless of how much you depress the accelerator pedal or the brake pedal. The coefficient of friction between tire and dry pavement is typically 0.6, and a driver experienced with that value can usually guess the distance required to stop the car from any initial speed.

However, if the driver drives over ice, the coefficient of friction may be 0.1 or even lower and the tires can easily slip on the ice, and so the car can slide uncontrollably. Worse, the sliding can melt some of the ice. Then, with a layer of lubricating water beneath the tires, the coefficient of friction may be negligible. Worse still, the coefficient can be different on different tires, and the different amounts of friction on opposite sides of the car can cause the car to spin, especially if the road is tilted. In the video at the first of the following URLs, you can see drivers suddenly encountering ice on an overpass (bridge). Such a location is always the most dangerous because ice can form there even when the rest of the road is ice free. The reason is that the rest of the road can be kept relatively warm by the underlying ground, but only (cold) air underlies an overpass. So, a driver can be caught by surprise by the ice on a bridge. Hence the common road caution: Warning, bridges freeze first.

If the car is on horizontal road when the tires begin to slip on ice, the center of mass of the car will continue to move in its initial direction. Well, in any practical situation, it moves until the car runs into something. However, the situation is worse if the road has even a slight tilt (maybe only a few degrees), because then the gravitational force can slide the car downhill. If the driver guns the engine and rapidly spins the tires, the resulting melting just makes the situation worse. In the video at the second URL, watch the driver maneuver the car and then gun the engine as the car begins to slide left to right down the hill. Definitely not a good idea. The car becomes a pinball as it bounces from impact to impact, almost as though the driver was trying to maximize his score in a game called “Let’s destroy everything on the street.”

The third video shows a comical but extremely dangerous situation. One car crashes, and then the next car crashes into it, and then another car crashes. This is a chain collision in which car after car collides at the end of the chain, each time sending a pulse of additional collisions along the chain, as momentum and energy are transferred from car to car. These collisions are almost like the ideal ones discussed in textbooks because the friction between the tires and road can almost be neglected. (In the textbook jargon, the collisions are isolated, and we can conserve momentum. However, kinetic energy is certainly not conserved---just look at all the damage.)

There is a subtle danger in the chain collisions in second and third videos: Look at all the people who casually walk between the crashed cars. If they understood physics, they could run the “movie” in their heads and predict what will happen if yet another car hits the chain while they are walking between two of the cars. I like tee-shirt summaries for physics, and these videos provide an excellent one: Physics can keep you from getting squashed.

http://www.youtube.com/watch?v=bT9iL6cxGQ8&feature=PlayList&p=DF6AAF85AE4F4D8A&playnext=1&index=5 Overpass (bridge) freezes

http://www.youtube.com/watch?v=7pV7uKn6S4Y&NR=1 Let’s see: Your car is on an incline, the coefficient of kinetic friction is about 0.1, and the car is rotating. Should you gun the engine? Correct me if I’m wrong, but I think that is not a good idea.

http://www.youtube.com/watch?v=BM2gLjfE_3Y Chain collision
http://www.youtube.com/watch?v=a293u2g27CE&feature=PlayList&p=DF6AAF85AE4F4D8A&index=6
http://www.youtube.com/watch?v=_sXLvjRXdeE&feature=related 
http://www.youtube.com/watch?v=deRVwthMHzU&feature=related 
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1.202  Cars on ice – the 2010 video collection
Jearl Walker www.flyingcircusofphysics.com
Jan 2011 Cars on ice are always fun to watch because they are like a cartoon figure (say, the coyote in a Road Runner cartoon) who desperately attempts to avoid a danger (explosion, falling rock, etc.) but can only run in place, without being able to actually move forward. The driver in a sliding car disparately tries to drive out of danger but manages only to spin the wheels. Nature (or rather the lack of friction) dictates the car’s motion, totally ignoring the driver’s will.

Here is the latest set of sliding car videos. However, as always here at the FCP site, the challenge is not merely to watch humorous “eye candy” and then move on to the next video. Any Youtube viewer does that. Instead, the challenge here is, can you say anything intelligent about what you see? Can you spot anything curious? After all, the power of physics is that it gives you insight into events, raising you above the Homer Simpson level.

Ok, here is the first video. What can you say about it?

http://www.cnn.com/video/#/video/us/2010/12/19/wa.ice.sliding.cars.khq?hpt=C2 icy road, lots of collisions (slow to load)

Obviously, the trouble appears when the road is covered with ice because the frictional force between tires and ice is very low, even for snow tires with deep tread. We need friction in order for the vehicle to move in a controlled way. Indeed, in normal driving the force that actually propels the vehicle forward is the frictional force acting on the tires that are being turned by the engine (two wheels on a two-wheel drive vehicle, and four wheels on a four-wheel drive vehicle).

The engine sets up a torque on the wheels to rotate them, and the tires push backward against the road. The frictional force on the tires is in the forward direction, opposing the attempt of the tire to slide backward on the road. Thus, that frictional force is in the forward direction, propelling the vehicle.

Well, that is what should happen but if you tires are on ice and you “gun” the engine, the large torque on the wheels rotates them so rapidly that they overwhelm the frictional force and slip on the road. Then there is approximately no friction on the tires and you have no control over the motion of the vehicle. In several videos linked below we can hear and see the driven wheels spinning rapidly. The drivers are doing the exact wrong thing by gunning the engine (they are also damaging their transmissions).

The other way to eliminate the friction on the tires is to stop the wheels from turning by hard braking while the vehicle is moving. In many vehicles a computer (part of the automatic braking system, or ABS) prevents such “wheel lockup.”

Once friction disappears, a stationary vehicle remains stationary and a moving vehicle continues to move in its direction of travel at the instant of the disappearance, at least initially. Braking and increasing the fuel flow are then irrelevant because there is no friction on the tires. Well, that is the story on a flat road. On a slope, the story is a lot more fun because, once the friction disappears, the gravitational force on the vehicle can accelerate the vehicle down the slope. Then things get really interesting because the vehicle can begin to spin.

Obviously if the vehicle bounces off a curb or some other object, the impact can cause it to spin. And if the driver has initiated a turn just before the friction disappears, the vehicle will spin. But spinning can also occur because of a difference in the frictional forces on the front and rear of the vehicle. Here are two possibilities.

1. Suppose you are moving up an icy slope in a front-wheel drive vehicle, with the vehicle turned somewhat to your left, as drawn here.


As the vehicle slows, you unwittingly increase the fuel flow. The increase torque on the front wheels overwhelms the friction and those wheels then spin with no frictional force. The gravitational force is pulling the vehicle down the slope, but there is still some frictional force acting on the rear tires, which are not being rotated by the engine. The rear end is effectively pinned in place, and the gravitational force causes the front end to rotate around the rear. The front end then slides down the slope past the rear end, which sets up the spinning. The frictional force on the rear tires is then overwhelmed, and the vehicle spins as it moves down the slope.

 

2. Suppose that you are moving down the icy slope in the same vehicle, with the vehicle turned somewhat as drawn here.


The heavy load on the front end of the vehicle (due to the engine and also the downward tilt of the vehicle) makes slipping there less likely, but the motion of the vehicle has overwhelmed the frictional force on the rear wheels. Now the front wheels are effectively pinned and the gravitational force rotates the rear of the vehicle around them, setting up the spinning.

You can see an example of this second possibility in the following video, when the white car begins its slow descent down the icy slope, a few minutes into the video. When we first see the car, the driver has put on the brakes and turned the car somewhat clockwise in our view. The frictional force on the rear tires has disappeared, but there is still some friction acting on the front tires. The result in a scary clockwise spin of the car.

http://www.youtube.com/watch?v=rhZCyQ3emQg Cars and a bus on an icy hill in Seattle.

I’ll leave the explanation of the bus to you but will point out that the engine is at the rear and drives the rear wheels.

Here are several more cars-on-ice videos:

http://www.youtube.com/watch?v=7MPRmOUxRMY&feature=related Very scary video. Driver and passenger roll out of sliding car. (Slightly naughty word is used.)

http://www.youtube.com/watch?v=2lJDNNXzB9E&feature=fvw When you are sliding down a hill, should you press down on the gas pedal to accelerate?

http://www.youtube.com/watch?v=T0FjntOZV58&feature=related car on icy hill, then the driver on the icy hill, embarrassed and furious. (If you fall down hard on an icy slope, why would you stand up and try to walk?)

http://www.youtube.com/watch?v=mjMZaNk3A8M&feature=related Seattle street

http://www.youtube.com/watch?v=9khlLNqhzEs&feature=related multiple spinouts on icy bridge
http://www.break.com/index/excavator-sledding-in-a-winter-wonderland-1979601 excavator sliding down a slope

http://www.youtube.com/watch?v=wYgW53lxrMQ&feature=fvw CBS News runs the video of the Seattle bus just before its crash

http://www.youtube.com/watch?v=4-m59vNK6gk&feature=related same CBS video

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1.203  Penn and Teller magic, with Teller as possible road kill
Jearl Walker
www.flyingcircusofphysics.com
October 2007 You already know the see-saw effect: you and a friend can balance each other on a see-saw such that the board is horizontal (with your feet off the ground). You and your friend are each pulled downward by the gravitational force with a size that we commonly call weight. The force on you tends to rotate the board downward on your side, and we calculate that tendency as a torque, which is the product of your weight and your distance (the lever arm) from the board’s pivot point.

If you push yourself outward on the board, away from the pivot, your weight does not change but the torque it creates increases because the lever arm increases. With your friend on the opposite side of the board, there is a competition of torques. You can keep the board horizontal only if you and your friend adjust the lever arms to balance the torques.

So it goes with a dramatic stunt by the famous magic duo Penn and Teller, who know lots of physics. Watch the video and then come back here.

http://www.youtube.com/watch?v=_g7jEyonsqs

In case you cannot watch YouTube, let me briefly describe the stunt. Penn shows us a commercial cargo truck (“eighteen wheeler”) that will be pulled over Teller, who will lie on the street. Penn escorts us to the back of the long truck, swings open the back door, and explains how the truck has been loaded with heavy blocks. Then he climbs into the driver’s seat in the tractor (front) part of the truck, and Teller lies down in front of the first of the double wheels of the trailer part of the truck. As horrible as it sounds, Penn pulls the trailer over Teller, wheel by wheel, as Teller winces, and yet Teller is unhurt.

There are no mirrors, and Teller is really there spread out on the street. So, how is the stunt done?

In short, the wheels that roll over Teller are fake and bear no weight. Only the wheels on the far side are real and actually bear weight. When Penn opens the back of the truck, he shows us only the far side of the cargo area, where the heavy blocks are stacked. We, of course, assume that the left side also has heavy blocks, but the only blocks within the truck are near the weight-bearing wheels on the far side.

As we see when Penn explains the trick, additional weight lies on a platform built outward on the far side of the truck, initially out of our sight. The weight-bearing wheels support that weight also. The situation is like you and a friend balancing on a see-saw. The line running through the weight-bearing wheels is the pivot of the see-saw. The trailer portion of the truck and the blocks inside the truck are effectively you on the see-saw. And the weight on the platform is effectively your friend on the see-saw. The magicians have carefully balanced the torques on the two sides of the pivot line.

The tractor that pulls the trailer part of the truck must have been altered in order to pull along the pivot line rather than at the normal central point. Otherwise, the pull would upset the balance of torques, and then Teller would end up being road kill, flattened into a bloody mess on the street. But the stunt ends up being fun, not horrible.

Indeed, physics is the fun of magic, because we laugh when we see a performer seemingly break the laws of nature while smiling at us with a twinkle in the eye.


1.204  Implosion demolition
Jearl Walker www.flyingcircusofphysics.com
Nov 2007    Large old buildings are brought down by explosions, as you can see in the following video links. However, if an engineer does not use physics in setting up and executing the explosions, heavy concrete chunks will fly all over the neighbors, which can make them hopping mad. Or the building will fall over onto the engineer, which is professionally embarrassing (and also lethal).
A better plan is to arrange for the building to pull itself down, with the debris landing in a pile in the middle of the building’s footprint (the ground area occupied by the building). The technique has been likened to a foot sweep in judo, in which you first sweep a foot out from under your opponent to eliminate that foot’s support, and then you rotate the opponent around the remaining foot. Actually, in a well-executed foot sweep, your force and gravity both create torques to rotate the opponent around that foot.

In building demolition, one plan is to knock out the support of the floors near the center of building first, and then progress outward. The weight of the floors causes the floors to rotate around the remaining supports along the outside of the building, and that motion pulls the outer walls toward the center of the building. Floors then crash down onto lower floors in what is called pancaking. Even if a lower floor has not lost its support, the impact of a higher floor onto it produces such a huge force that the lower floor’s support collapses.

A demolition engineer must be very skilled in placement of the explosions. Usually, a hole is drilled in a vertical concrete column and then dynamite or some other explosive is packed into the hole. Sandbags are packed around the hole to contain the explosion --- the idea is not to send debris everywhere like a grenade, but to weaken the column so that the weight it supports causes it to buckle. Sometimes cables are run between adjacent floors so that when the lower floor sags, it pulls on the outer wall at the juncture with the next higher floor.

Although this technique of bringing down a building is called implosion demolition, the collapse is actually due to explosions. However, the term implosion might still be appropriately descriptive because the building falls in on itself rather than on the old-folks home next door. And the explosions are contained to be within the building’s footprint and do not send chunks of concrete through the windows of the old folks.

Careful consideration of the physics in the collapse of structure is needed. Otherwise you get the very embarrassing situation shown in some of the following videos.

http://www.metacafe.com/watch/176540/china_demolition/ All fall down, except for one

http://www.metacafe.com/watch/209655/jackass_demolition/ Not all the demolitions are well thought out (and there are some scenes that have nothing to do with building demolitions).

http://www.aerialpics.com/C/implosion.html Click to see aerial photos and videos. My favorites: Detroit Edison Conner Creek implosion demolition of 1996: building plus tall stacks --- way cool

http://www.youtube.com/watch?v=fiNrzmbdC1Q Well, suppose things just don’t work out.

http://www.metacafe.com/watch/210787/destroyng_is_nice/ Nice camera work

http://www.controlled-demolition.com/default.asp?reqLocId=7 Videos, stories. Click to watch the collapse of the Villa Panamericana & Las Orquideas public housing complex in San Juan, Puerto Rico, which set the world’s record for “the most buildings to be demolished simultaneously with explosives.”

http://www.implosionworld.com/ Homepage of ImplosionWorld.com . Includes videos, photos, essays, and links.

http://www.youtube.com/watch?v=eUIdf4UJ3_4 Excellent shot of building

http://www.youtube.com/watch?v=ZlGmnKvOhlg

http://www.youtube.com/watch?v=0Fpv6pxsrOQ Video from a hight point

http://www.youtube.com/watch?v=TdEnb-ifIbU Dallas building collapse
http://www.youtube.com/watch?v=51TQ1PrYf7M Demolition of circular sports stadium

http://science.howstuffworks.com/building-implosion.htm Essay plus videos of implosion demolition from HowStuffWorks.

http://www.ireport.com/docs/DOC-47439
http://www.youtube.com/watch?v=7Ng5qwtR59A&NR=1
http://www.youtube.com/watch?v=NqRN63iDTqA&NR=1
http://www.youtube.com/watch?v=-1X8j53U1So Building collapses when the foundation on one side gives way
http://news.bbc.co.uk/2/hi/uk_news/7628412.stm building demolition
http://news.bbc.co.uk/2/hi/uk_news/7579430.stm Cooling towers demolition
http://news.bbc.co.uk/2/hi/uk_news/scotland/7516356.stm building demolition
http://news.bbc.co.uk/2/hi/asia-pacific/7698202.stm Chinese dam demolition

http://news.bbc.co.uk/2/hi/asia-pacific/7697582.stm Three Gorges bridge demolished

· Loizequx, J. M., and D. K. Loizeaux, “Demolition by implosion,” Scientific American, 273, 144-153 (October 1995)
· · · Marjanishvilli, S. M., “Progressive analysis procedure for progressive collapse,” Journal of Performance of Constructed Facilities, 18, No. 2, 79-85 (1 May 2004)

1.204  Rolling a building down the street
Jearl Walker www.flyingcircusofphysics.com
Sep 2009   One of the techniques in judo for making your opponent fall over is a foot sweep in which you bring your right foot smartly against his left foot to sweep his foot off the mat. You can simultaneously pull him to your right with your hands, which already grasp his uniform, but even if you don’t pull, he will fall down to your right just because of the foot sweep.

Initially he is stable because his center of mass is located above the area on the mat between his feet. The gravitational force pulls down on every part of his body, but we can say that it collectively acts at the center of mass, the center point of the body. With the center of mass located above the support area, the gravitational force cannot rotate the body around either foot. In the language of both physics and judo, there is no torque to cause rotation.

However, once you sweep out the opponent’s left foot, the support area shrinks to just the area of his other foot and the downward pull from gravity is then offset from that support area. Now there is a torque, and the gravitational force rotates your opponent around that foot and down to the mat. Here is a diagram of the situation from the textbook that I write (Halliday, Resnick, and Walker, Fundamentals of Physics). The gravitation force is the downward force acting at the center of mass (labeled com). The pull from my grasp on his uniform is the rightward pull at chest level. And the distance d is the offset (or lever arm) of the gravitational pull from his supporting foot still on the mat. In short, if you can set up a lever arm like this, the gravitational force is enough to make him fall.

Here is a similar fall but in a very different setting. (I thank Chris and Lou Slavik who sent me this link in response to one of the Flying Circus of Physics newsletters.) A building is to be brought down by exploding its support columns. Such explosions must be controlled and, most important, timed correctly so that the building loses its support simultaneously on all four corners and then falls straight down in a pancake collapse. However, as you can see in the video, the timing was off and the building fell down very much like a judo fighter in a foot sweep. Then, because the upper floors were still rigidly connected, the building went into a roll. Things are pretty embarrassing when you end up rolling a building down the street, like a ball in game of bowling.

http://www.youtube.com/watch?v=coZZdDeECow

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1.204 Building topples over
Jearl Walker www.flyingcircusofphysics.com

Dec 2009   Here are photos and drawings (sorry, I don't know who gets credit for them) that show a 21-story building after it fell over like a domino. If the building-to-building spacing had been small enough, there could have been a domino effect on a line of buildings. Thankfully, there was no such effect and no one was hurt or killed.
    An underground parking lot was being dug out on one side of the building, with the dirt piled on the opposite side. Thus there was a pressure difference on the two sides of the building, on the concrete pilings that secured the building in the ground: lower pressure on the dug-out side and higher pressure on the piled-up side.
When rain soaked the ground and also eroded the dug-out side, the pressure difference became so large that sone of the pilings broke and the building leaned toward the dug-out side, which bent and broke the rest of the pilings. In the latter photos, you can see those pilings --- some have horizontal breaks and other have breaks that travel across and down the piling. The latter broke while being bent.


 








































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1.205  The Wheel of Death
Jearl Walker www.flyingcircusofphysics.com
Dec 2007   
The Wheel of Death consists of a large rotating apparatus driven by men running or climbing inside attached cylinders. The sight awakens some existential fear in me, throwing me back to the old Pink Floyd song “Welcome to the machine.” The following two links take you to a surreal, gothic performance of the Wheel of Death by the entertainment group Cirque du Soleil. Watch the front apparatus but don’t be startled by the sudden reversal in the rotation direction after about one minute---two videos were blended there.

http://www.metacafe.com/watch/184819/wheel_of_death/

Now note that the front wheel consists of two opposite arms that rotate around a central axis like arms on a clock face. At the outer end of each arm is a rigidly attached cylinder that holds a performer. From the audience perspective, we see through each cylinder, along the central axis, and thus we can see a performer stand within a cylinder or climb its side.

The performers somehow cause the arms to rotate, and then each must scramble to maintain his balance as the cylinders move around in a large circle. However, anyone can make that observation and marvel at the performance. Can physics say anything more enlightening than just “Wow”?

The video opens with the wheel already rotating, but later on we get to see it started up from rest. I spotted two ways the rotation is begun and then maintained.

Unbalanced arms

Because they are at opposite ends of the two rigid arms, the two men are effectively on a see-saw (or balancing board). Each provides a downward force on the see-saw because a gravitational force acts on him. The force due to the man on the left produces a torque that tends to rotate the arms counterclockwise. The force due to the man on the right produces a torque that tends to rotate them clockwise. If the men were at equal distances from the rotation axis about which the arms rotate, these two torques would just cancel and the arms would not rotate. However, watch carefully in the first part of the video.

The man who is moving downward leans on the outer cylinder wall or climbs it, which means that he is as far from the rotation axis as he can get.

The man who is moving upward leans on the inner cylinder wall or climbs it, which means that he is as close to the rotation axis as he can get.

That imbalance of positions means that there is a net torque that is dominated by the descending man, which maintains the direction of rotation.

Later in the video, when one man is running over the top of his cylinder, the torques are still imbalanced when the arms pass through the horizontal orientation. That man is farther from the rotation axis than the other man, who is leaning on or climbing the inner wall of his cylinder.

Shifting mass

The other mechanism I see in the performance is similar to pumping a swing, which has long been a favorite topic of physicists. As I explain in The Flying Circus of Physics, when you pump a swing, you shift your mass in a strategic way during the swing’s motion. Suppose that you are standing on the swing. When you are high in the swing arc, you squat. When you swing through the low point, you stand. The result is that you build up the extent of the arc --- that is, you go higher and higher.

We can explain the increase in terms of either energy or angular momentum. For the former, you must work hard to stand when you go through the low point where you are moving fast. The energy you produce in standing goes into the speed of the swing. When you reach the slow part high on the arc and squat, squatting is almost effortless.

In terms of angular momentum, you are like an ice skater spinning on point. If the skater brings mass closer to the rotation axis by pulling in a leg or arm, the skater spins faster. Briefly, the angular momentum is the product of the mass distribution and the angular speed. When there is no torque to change the angular momentum, then any reduction in the mass distribution must be offset by an increase in the angular speed. So, the ice skater speeds up.

In the Wheel of Death, when the performer runs over the top of his cylinder, notice that whenever he moves through the bottom of the circular path, he must move closer to the rotation axis. That requires work, and he transfers energy to the rotation. When he passes through the high point of the circular path, he works against the gravitational pull and stores gravitational potential energy in the system. When he next rotates down, that energy is put into the rotation.

http://www.youtube.com/watch?v=Qfl_Imectvo

http://www.youtube.com/watch?v=aZJwY4aA2ps

http://www.youtube.com/watch?v=SeksowQIZFQ

http://www.youtube.com/watch?v=QYwjGhHj9LE&feature=related

http://www.youtube.com/watch?v=f4YnwZUirio&feature=related
http://www.youtube.com/watch?v=O8y0SDQjMQ8
Wheel of Death blindfolded

http://www.youtube.com/watch?v=C4DfSBnBR08 

 

1.206  Falling cranes --- from silly to deadly
Jearl Walker www.flyingcircusofphysics.com
April 2008    
First the silly stuff. After a car was driven off a wharf and the driver rescued, a tow truck with a long crane was brought in to lift the car from the water. The cable from the crane was attached to the submerged car, and then the crane’s motor was engaged to pull the car up from the water. In the following link, we can see photos of the process.

http://www.snopes.com/photos/accident/crane.asp

In the second photo, the car has just moved above the water surface, and water is draining from the open door. In the next photo, the car is level with the wharf and apparently on its way to safety. But then in the fourth photo, we see the car crashing back into the water, tipping the tow truck over and into the water. Very embarrassing.

So, what went wrong? Obviously the load was too much for the crane on the tow truck, and the truck rotated around the tires closest to the wharf edge. Anyone can say that much, but the power of physics is that you say something more. The accident involves two principles of physics.

When an object is submerged, a buoyancy force pushes upward on it. You notice that force when you swim --- you feel weightless. In fact, if you were to stand on a weight scale while floating, the scale would read 0. Of course, your body’s mass is the same, and so is the gravitational force on you. But when you are submerged, there is an upward buoyancy force on you due to the water pressure against your body.

When the car in the photos was submerged, there was an upward buoyancy force. The car was not weightless like you because the materials in it, such as the metal parts, were far too dense to float in water. Still, the buoyancy force reduced the effective weight of the car, perhaps by 25%. However, once the car was lifted out of the water, that weight reduction was eliminated, and the force on the crane was the full car weight. Well, actually until the water drained out of the open door, the weight was a bit more than the full car weight.

The second physics principle here involves the lever arm of the crane. This is the horizontal distance between the base of the crane on the truck and a vertical line through the car. You can easily feel the effect of a lever arm by picking up a book with a straight arm. Start with the arm directly downward and rotate it until it is horizontal. The lever arm is the horizontal distance between the point of rotation at your shoulder and a vertical line through the book. As you bring the arm up to be horizontal, the lever arm increases, until it is the full length of your arm. Notice how the difficulty of holding the book also increases. We measure the difficulty of such a lift in terms of a torque, which is the product of the book’s weight and the lever arm. So, when you lift your arm, the torque increases.

In the first photo of the car, the tow truck’s crane is angled downward and the torque on the crane was relatively low for two reasons: (1) the lever arm was short and (2) the car’s weight was effectively reduced by the buoyancy force. However, as the car was pulled from the water and the crane arm was lifted to the horizontal, the torque dramatically increased until it was large enough to rotate the truck counterclockwise around the wheels nearer the water. Until that failure point was reached, the truck’s weight was enough to counter such a rotation.

To rescue the car and the tow truck, an even larger crane truck was brought in, as you can see in the next several photos. However, when the photos were posted on the web a few years ago, someone altered the photo of the larger crane truck to show that it too was rotated around its wheels and into the water when it tried to lift the first truck. We all laughed at such a double failure before we realized that the photos were faked.

Failure to appreciate the role of buoyancy when lifting a vehicle from water may be common. Here are two more links where we see a crane being rotated over the edge and into the water once the vehicle on the end of the line clears the water. In one of the links, I am amazed that no one was killed.

http://www.youtube.com/watch?v=O5X_Z9vEORU&NR=1 crane pulled over into river while trying to lift a bus

http://www.youtube.com/watch?v=Q5GY6Efkyjo&feature=related Crane pulled over into lake while lifting something from the water.

James Bond car
Here is a counterexample, where someone is being smart about lifting a car from water. During the current filming of the next James Bond movie, Bond's Aston Martin DBS was accidently driven off a road and into Lake Garda in Italy as the car was being driven to the film site. The driver was easily rescued but the car was more difficult. Here is a link to a photo of the car after it had cleared the water. 
http://news.bbc.co.uk/2/shared/spl/hi/pop_ups/08/entertainment_enl_1208640064/html/1.stm
Notice how large, both in length and in mass, the crane and truck are. You can see the break in the fence where the car must have left the road. It probably was traveling at a fairly high speed and thus landed in the water about where we see the boat in the photo. So, the crane had to reach out with a fairly long lever arm and then lift the car from the water. Understandably, the movie crew was anxious to lift the car without any additional trouble because apparently this was the only Aston Martin DBS available for the movie and they had to quickly restore it to not only working conditions but also to the elegance that we would expect of a James Bond car.
 
Outriggers

Crane trucks usually come with outriggers --- legs that extend outward from the side of the truck on both sides. The purpose is to decrease the chance of the truck rotating around its side. The situation is similar to that of a domino made to stand upright on a floor. The domino, with a fairly narrow base on the floor, is moderately stable. But if we substitute a much wider block, the stability is dramatically increased ---- it is more difficult to rotate a child’s block around one edge than a narrow domino around one edge.

Often the crane is extended from the rear of the truck because the truck’s long length can decrease the chance that the truck will be rotated over. Still, accidents happen as can be seen in the following links.

http://www.youtube.com/watch?v=aZoZSzT0W9s&feature=related Crane that has fallen into a house

http://www.youtube.com/watch?v=zweFG0cG7XE&feature=related Crane righting crane. Note the crane on the left keeps a short lever arm.

http://www.local1259iaff.org/craneaccident.htm Crane toppled over while trying to lift an air conditioning unit from the roof of a store in Texas City.
http://www.americacranetraining.com/accident.htm Photos of toppled cranes

http://www.youtube.com/watch?v=LWlj5nEqRCE&NR=1 Crane collapses while attempting to lower a very heavy load onto the top of a building

http://www.youtube.com/watch?v=LuNjOfan0zA&NR=1 Proper use of a crane in an amazing rescue of a man trapped in a pickup truck that was almost flattened by a heavy cargo truck

Tower crane in New York City

Last month a tower crane fell over at a construction site in New York City. As the tall crane rotated toward the ground, a lower section with a height of about 19 stories hit a residential building across the street from the construction site and stopped, but the rest of the crane snapped off and then hit two buildings before completely flattening a multiple-story townhouse.

Information about the accident is still being uncovered, but the focus of the investigation is on the stabilizing collars that were used to stabilize the tower portion of the crane. The tower is built upward as the building is built upward. To stabilize the tower, it is either anchored into a concrete base or bolted to a series of collars attached to the girder framework of the building.

The tower crane that fail depended on the collars. Early reports indicate that as one of the collars was being put into place near the top of the construction, it fell down along the tower, striking a lower collar and causing the tower to lean. Once the center of mass of the tower and the very heavy crane arm at the top moved off to the side of the tower’s narrow base, the whole apparatus was like an upright domino that had been pushed on its face, and nothing could stop the rotation until the apparatus hit a building. Physics is everywhere, even in tragic death.

 

http://forum.skyscraperpage.com/showthread.php?p=3412404 step by step construction of a tower crane
http://www.youtube.com/watch?v=V-MyHCaBKqk&feature=related Crane falls onto a car

1.207  Twining plants on a garden rod

Jearl Walker www.flyingcircusofphysics.com
May 2008
   Perhaps the finest example of my statement that “physics is everywhere” lies in the recently published analysis of climbing plants, that is, twining plants, which includes garden peas and morning glories. As most home gardeners know, these plants will spiral upward around a vertical rod stuck into the ground. The spiraling is too slow to see, even if you camp out near the plant with a basketful of sandwiches and plenty of beverages. But here is a link to a time-lapse video of a twining plant that reveals how the stem searches for something to climb:

http://plantsinmotion.bio.indiana.edu/plantmotion/movements/nastic/nastic.html choose “Morning glory twining” from the menu on the left. Click to activate the movie. Roger P. Hangarter at Indiana University

Yes, I know the plant is responding mechanically to its environment and does not think, but golly all that spinning around by the plant’s stem sure makes me think that the stem could spiral around my leg and pull me down to the ground like some plant-based monster on a Doctor Who show.

However, the fact is that my leg is too thick for the stem to spiral around. That is, there is a certain upper limit to the thickness (or diameter) of a rod around which the stem can spiral and my leg exceeds that limit. Now, that is most curious because, even though this is biology stuff, a physicist starts to question, “Upper limit? Why an upper limit? What is determining an upper limit? Why can’t the diameter be anything, even the diameter of a tree?” See, that is the way a physicist thinks --- if you say there is a limit, a physicist immediately challenges it. Normal people would just say “ok” and then go off to watch some reality show on television.

Darwin noticed the upper limit (he was not a physicist but he should have been with this observation) for a certain climbing plant, which can twine around rods of radius 3 millimeters but not around rods of radius 5 or 6 millimeters. In 2006, Alain Goriely of the University of Arizona in Tucson and Sebastien Neukirch of CNRS and Universite Pierre et Marie Curie in Paris carried the matter much further by constructing a two-dimensional model of a stem twining around a rod without friction. Here in a nutshell is their argument as I see it: The stem is curved under tension like the coil in a spring. If the stem is put on a rod that is more tightly curved, the free end of the stem can move around the rod as the stem grows in length. But if it is on a rod that is much less curved, the growth causes the stem to curve back on itself, and then the stem just forms a loop on the side of the rod.

Let’s take a coil in a metal spring (or Slinky) and snip off one fourth of a full circle. Then let’s hold that section vertically on a table with the free ends (the tips) touching the table. The section is still under tension, just as it was in the spring, and that is way it is still curved. If you push down on the top of the curve, to try to spread the tips, you increase the tension and the section resists you. If, instead, you try to move the tips toward each other, you also increase the tension and the section resists you. In short, the section “wants” to have the shape it already has, to keep the tension as low as possible.

The stem on a twining plant is similar. There is an arc that is under tension. One end is free of the arc will move as the stem (and the arc) grows longer. Now if the arc is on a rod that is more tightly curved than it is, then as the arc grows in length, the free end slips around the rod in order to keep the tension as low as possible. However, if the arc is on a wide rod, the stem keeps the tension low by moving the tip under the arc, so that the arc begins to form more of a complete circle. Well, that means that the stem doesn’t wrap around the rod and thus cannot climb the rod.

The stem is not smart and yet it can mechanically sense how curved the rod is. Goriely and Neukirch calculate a critical rod radius that separates climbing from non-climbing. If the radius of the rod exceeds about 3.3 times the radius of the stem’s arc, climbing cannot occur unless there is substantial friction between the stem and the rod. If there is enough friction, the stem might be able to climb a fairly wide rod.

Goriely and Neukirch did their calculations in two dimensions, using the circular cross section of a rod. Why not test their ideas in three dimensions by growing some twining plants such as morning glories, on a variety of rods, from thin to thick and from slick (as with plastic) to ones with friction (as with wood). Let me know what you find.

Physics is everywhere, even in a garden of morning glories.

· · · Goriely, A., and S. Neukirch, “Mechanics of climbing and attachment in twining plants,” Physical Review Letters, 97, article # 184302 (4 pages) (3 November 2006)

http://www.oeb.harvard.edu/faculty/holbrook/people/alex/Website/twining/twiningMovieQt.htm another time-lapse movie showing plants twining. Alex Cobb in the Holbrook Laboratory. Requires Quick Time.

http://math.arizona.edu/~goriely/index.html home page for Alain Goriely

http://math.arizona.edu/~goriely/res-twining.html Alain Goriely’s page on the twining of climbing plants

http://www.lmm.jussieu.fr/~neukirch/twining_plants.html Diagrams and brief description by Neukirch
http://math.arizona.edu/~goriely/Press/Climbing%20plants%20get%20wrapped%20up%20(November%202006)%20-%20News%20-%20PhysicsWeb.pdf news item about the paper by Goriely and Heukirch.

http://math.arizona.edu/~goriely/Press/String%20Theory%20for%20Plants.pdf news item about the paper

http://math.arizona.edu/~goriely/pub.html




1.208  Indiana Jones and the Kingdom of the Crystal Skull

Jearl Walker www.flyingcircusofphysics.com
May 2008  Details of the new Indiana Jones movie (due out on May 22) are closely guarded, but speculation based on the released title is that it centers on the crystal skulls that first appeared in the hands of archaeologists and would-be archaeologists about 60 years ago. Such a skull, which resembles a human skull, was carved from a quartz block and then ground into shape. Probably the most celebrated crystal skull was one that appeared mysteriously in 1992 at the Smithsonian in Washington DC. That larger-than-life skull was attributed by the anonymous donor to be an Aztec relic. In anthropology language, it was thought to be a pre-Columbian, Mesoamerican relic. Here is a link to a photo of the skull:

http://www.archaeology.org/image.php?page=0805/etc/jpegs/indy1.jpg

Plenty of other crystal skulls have appeared over the years, sometimes with great mysticism and even hints of alien origins. The one that showed up at the Smithsonian was investigated by Jane MacLaren Walsh, an anthropologist who has recently published an account of her findings. Her challenge was this: Was the skull truly a pre-Columbian relic or was it carved in modern times? That is, is it actually a relic or is it only a fake?

The answer to the challenge lay in the microscopic details of how the skull’s surface was abraded when it was shaped and then polished. Of course, those details are too small to be seen by the eye or even by means of a magnifying glass or even by means of an optical microscope. To see enough of the details, Walsh needed a scanning electron microscope (SEM) in which the waves are not light waves but electron waves.

Here is the basic reason she needed to use electron waves. The wavelength of the waves used in any microscope sets the resolving limit of the instrument. That is, an optical microscope cannot reveal details that are smaller than the wavelength of the light waves it uses. For example, if blue light is used, with a wavelength of about 400 nanometers, then the smallest detail that can be resolved is about 400 nanometers. Using the somewhat shorter wavelengths of ultraviolet light can improve the resolution but not by much.

However, the resolution can be greatly improved if the waves are electron waves because the wavelengths can be so much smaller. For example, the wavelength of the electrons in a scanning electron microscope might be only 1 nanometer. An electron’s wavelength depends on its speed --- a greater speed means a shorter wavelength. The speed is set by the acceleration the electrons undergo when they move through an electric field within the microscope. Thus, an operator can select the electron wavelength by selecting the strength of the electric field --- a stronger field results in a greater acceleration, a greater final speed, and a smaller wavelength. For many practical reasons, the smallest wavelength in an SEM is about 0.1 nanometer.

Now, the idea that an electron is a wave rather than a particle might surprise you. Regarding an electron as being a particle is usually a lot easier --- a tiny particle zips around like the ball in a pinball machine. But the fact is that when we say that an electron moves from one point to another, it is a wave that makes the trip, not a particle. (An electron is a particle only in the sense that when it interacts with matter, such as the screen in a conventional (tube) television set, the interaction is at a point.) I think the wave-like nature of an electron is both way cool and way unnerving, especially considering that I have lots of these things in my body. I just feel less substantial when I think I consist of waves.

To investigate the crystal skull from the Smithsonian and two similar skulls from the British Museum, Walsh first needed to make a mold of the skull surface. She also made a mold of the surface on an artifact that had already been firmly established as being pre-Columbian. Making these molds requires that silicone gel be spread over a surface, allowed to harden, and then lifted away so that it carries an imprint of the microscopic structures on the surface. The mold surface is then coated with a very thin layer of gold to provide a conducting surface through which electrons can move, so that charge does not build up on the mold surface and then deflect the incoming electrons in the SEM. When the electron beam is turned on, the electrons scatter from the microscopic irregularities on the mold surface. As they then land on an electron detector, they build up a magnified image of those irregularities that we can see.

The feature that interested Walsh was the microscopic abrasion lines that were ground across a skull’s surface when the skull was originally shaped and then smoothed. Here is a typical SEM image of an abrasion line on the artifact that was known to be pre-Columbian. Note first that the distance of one nanometer (1 nm) is marked on the image. Then note that the abrasion line is rough (uneven), presumably because the abrasion was made by a stone file grinding sand across the quartz.
http://www.si.edu/opa/insideresearch/photo_pages/V9_CrystalSkulls.html_P-11Left.html

Here, next, is a typical SEM image of two abrasion lines on the Smithsonian crystal skull. Note that these lines are uniform and parallel.
http://www.si.edu/opa/insideresearch/photo_pages/V9_CrystalSkulls.html_P-11rightMED.html

The conclusion is this: The Smithsonian skull and the British Museum skulls were not made by pre-Columbian artisans grinding sand across the quartz. Instead, they were made with modern lapidary machines using rotating wheels, probably composed of tiny industrial diamonds that scoured out neat and parallel trenches in the quartz.

Well, that is reality, but the point of an Indiana Jones movie is, of course, that we suspend reality for about two hours. So, in those two hours, if my hero wants to believe that a crystal skull is an alien artifact with metaphysical properties, then hey, I’m all for it. I like the fun of the Sherlock-Holmes investigation by Walsh, but I am also a huge fan of Indiana Jones fighting off the bad guys.

· Walsh, J. M., “Legend of the Crystal Skulls,” Archaeology, 61, No. 3, 36-41 (May/June 2008), available at http://www.archaeology.org/0805/etc/indy.html
· Inside Smithsonian Research, Quarterly Newsletter on Science, History and the Arts, No. 9 (summer 2005), available at
http://www.si.edu/opa/insideresearch/articles/V9_CrystalSkulls.html



1.209  Alligator death roll
Jearl Walker www.flyingcircusofphysics.com
Alligator death roll
Jul 2008  An alligator (as in this image by nothneeds needed) has conical teeth and strong jaw muscles, which are good for clomping down hard on its prey but almost useless for chewing. So, when it grabs a large prey, it suddenly rotates in the water, violently twisting the prey to rip off an edible chuck. However, this death roll seemingly violates physics because … the alligator rotates without any external force causing it to rotate. Now, an alligator may be fierce (and really ugly too), but it has a keen devotion to the laws of physics. So, how can it roll without violating any of those laws? Here are some links showing death rolls (don’t worry --- no animals are killed).

http://www.youtube.com/watch?v=6BbkhDo1nRA&feature=related
http://www.youtube.com/watch?v=-9Z_UYLsvjk

http://www.youtube.com/watch?v=TnLQVPU2TC0&feature=related

http://www.youtube.com/watch?v=LqnKS6K8vdY&feature=related

The next time you go swimming, pretend that you are an alligator and try to undergo a death roll. Float face down with your arms pressed against your sides (an alligator in a death roll has its legs pressed against its sides). Without flapping your hands or legs, try to rotate around a horizontal axis that extends between your head and feet. For example, you might rotate your head up to the right in a counterclockwise rotation around the axis. However, that simply makes the rest of your body (your trunk and legs) rotate slightly to the left in a clockwise rotation around the axis.

Here’s the reason. We associate a quantity called angular momentum with a rotation. Its value depends on the angular speed and the way the mass is distributed relative to the rotation axis. However, all we need here are two ideas: (1) Angular momentum is positive for a counterclockwise rotation and negative for a clockwise rotation. (2) When several parts of a body rotate, the net angular momentum is the sum of the individual contributions of angular momentum from those parts.

Initially, when you are just floating, you have no rotation and thus have zero angular momentum. The only way that your angular momentum can change is if a torque (due to some force) is applied to your body. Another swimmer could push on you, rolling you over. Or you could push against an object, say, the side of the pool, to get a torque that would roll you over. But, if you are just floating by yourself, there is no such torque to roll you over and change your angular momentum. So, it has to continue to be zero. If your rotate your head counterclockwise so that, at least briefly, it has positive angular momentum, then the rest of your body has to rotate clockwise so that it has just as much negative angular momentum, so that the total continues to be zero.

Of course, twisting your head in one direction and making your body rotate in the other direction is not a smart thing to do in public. If an alligator did that, it would just hurt itself every time it tried to eat.

So, how does an alligator roll itself over while maintaining zero angular momentum? It knows a trick --- it does not keep its head, trunk, and tail in a straight line (along a single axis) as you keep your head, trunk, and legs in a straight line. Instead, it angles its head off to one side, say, the right side, and angles its tail off to that same side. From overhead, the body roughly forms a flared letter “c.”

The alligator then rapidly rotates the three body parts in the same direction, say, counterclockwise. The head rotates around an axis along the head. The trunk rotates around an axis along the trunk. And the tail rotates around an axis along the tail. Because all three rotations are in the same direction, counterclockwise, the net angular momentum is positive.

It can do that and still have zero angular momentum because (and here is the big secret) the c-configuration rotates in the clockwise direction giving a negative angular momentum. The net angular momentum (positive for each body part and negative for the c-configuration) is zero during these rotations.

The c-configuration rotates around a horizontal axis that runs down through the letter c as viewed from overhead, somewhat like the straight line that is superimposed on the letter c to represent cents ¢. The three body parts go through a full rotation in a death roll, but the c-configuration rotates only about 1/10 as much and may not be noticeable in the videos of a death roll.

The extent of the rotations depends on how mass is distributed relative to the rotation axis. The head’s mass is pretty much on the rotation axis through the head; the trunk’s mass is pretty much on the rotation axis through the trunk; and the tail’s mass is pretty much on the rotation axis through the tail. So, those three rotations are large. However, in the rotation of the c-configuration, a lot of the mass (especially that of the trunk) is pretty far off the rotation axis. That means that the configuration needs to rotate only a little bit in order to contribute enough angular momentum to keep the total at zero.

What I have described here is an alligator death roll. A gater death roll is different --- that is what a student at the University of Florida at Gainesville (the “home of the gators”) does when thrashing about on the floor after a tough physics exam, especially one based on the textbook I write. If you have a photo of someone (or an entire class) undergoing a physics death roll, send me a photo and I’ll post it.

· ·  Fish, F. E., S. A. Bostic, A. J. Nicastro, and J. T. Beneski, “Death roll of the alligator: mechanics of twist feeding in water,” Journal of Experimental Biology, 210, 2811-2818 (2007). Available at

http://darwin.wcupa.edu/~biology/fish/pubs/pdf/2007JEBDedathRoll.pdf  

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