The Top That Flips Itself Over: Tippe Tops, Standing Eggs, and the Rattleback That Spins Backward

There is a famous photograph of two of the greatest physicists of the 20th century bent double over a tiled floor. Wolfgang Pauli, who gave the world the exclusion principle, is crouched with his hands on his knees. Niels Bohr, who built the first quantum model of the atom, is leaning in beside him with his hands clasped. Between their shoes is a toy about the size of a walnut, and both men are watching it as if it might explain the universe.

The toy is a tippe top, and what it does looks like cheating. You spin it on its round bottom with the little stem pointing up. For a few seconds it behaves like any top. Then it starts to lean, the stem tips toward the table, and suddenly the whole thing heaves itself over and keeps spinning upside down on the stem, with its heavy round body now riding high in the air. It has lifted its own center of mass, apparently by itself.

The tippe top has two strange cousins. A hard-boiled egg spun on its side will rise up and spin on its end. And a canoe-shaped piece of stone or plastic called a rattleback will happily spin one way, but if you spin it the other way it shudders, stops and turns back the way it “wants” to go. All three kept serious mathematicians busy for decades, and the secret ingredient in each is the same unglamorous thing: friction.

A lapsed patent and a fruit on a stalk

The tippe top is older than its fame. In October 1891, a woman named Helene Sperl from Munich filed a German patent for a Wendekreisel, a “turning top,” that described the inversion trick in words. The patent ran out the following July because the fee wasn’t paid. Christian Ucke of the Technical University of Munich later tried building the tops drawn in the patent and found that none of them seemed to work, which suggests Sperl had a working model she simply didn’t describe correctly.

The toy was then forgotten until about 1950, when a Danish engineer named Werner Østberg reinvented it. According to the Vendsyssel Historical Museum in Hjørring, Denmark, he got the idea on a visit to South America, where he saw people spinning a small round fruit by its stalk. The fruit would spin for a moment and then flip over to spin on the stalk. Østberg had the toy made in plastic, named it the tippetop, patented it in several countries, and watched it take off.

The craze that distracted Copenhagen

In Denmark the tippetop became a genuine mania. A Danish radio feature broadcast in 1997, later reproduced by the physics site FYSIKbasen, recalls the newspaper coverage of the time. The tabloid Ekstra Bladet reported that respectable professors at the Polytechnic had dropped their normal work and were spinning tops day and night with stopwatches and slide rules. A sculptor wondered in a Politiken essay whether the whole Earth might once have flipped over like a tippe top, swapping its north and south poles.

The same feature says that when Winston Churchill visited Denmark, the press photographed him and Niels Bohr playing with one, and that neither could immediately say why it flipped. One paper joked that the two men had now settled the tippe-top problem and could go back to atoms and the situation in Egypt, respectively. Danish state radio then gave the question a full slot: Bohr’s son Aage, himself a future Nobel laureate, explained the top on the science program Månedens videnskab, and listeners were told to have a tippe top and a little powder ready by the loudspeaker so they could follow the tracks it left. Østberg kept a scrapbook of the press coverage, with clippings from 1951 and 1952. It’s now held by the Vendsyssel museum.

Bohr seems to have been genuinely taken with the thing. The Niels Bohr Archive holds another 1951 photo from Lund in which he demonstrates a tippe top to Sweden’s prime minister, Tage Erlander.

The physicists weren’t only playing. In 1952 the Dutch journal Physica ran back-to-back papers on the tippe top by C. M. Braams and N. M. Hugenholtz, and in 1954 William Pliskin published an analysis in the American Journal of Physics concluding that sliding friction “plays the primary role.” In France, according to the math magazine Tangente, the toy even became a demanding problem on the 1953 agrégation exam in rational mechanics, the competitive test for the country’s top teaching posts.

How a top turns itself upside down

The key is in the shape. A tippe top is a ball with a slice cut off, and its center of mass sits a little below the center of the ball. That small offset changes everything.

An ordinary top spins neatly on a point. A tippe top spins on a curved surface, and because the center of mass isn’t at the ball’s center, the point touching the table isn’t directly under the spin axis. As the top whirls, that contact point is dragged around in a little circle, sliding across the table. Sliding means friction, and friction pushing sideways at the bottom of a spinning ball creates a twisting force, a torque.

Here’s the clever part. When you spin the top fast, its angular momentum, the quantity that measures how much rotation it carries and in which direction, points almost straight up, and it stays pointing almost straight up. What the friction torque does is gradually tilt the body of the top relative to that vertical spin. The stem leans further and further over, the top passes through a moment where it’s spinning on its side, and then the stem touches the table. Now the stem is the thing sliding, friction acts at its tip, and that pushes the top the rest of the way up onto the stem.

If you watch from above, the top keeps turning in the same direction the whole time. But relative to the body of the top, the spin has reversed: the stem that pointed up is now pointing down, and the body is turning the other way around it.

What about that lifted center of mass? Raising the heavy part of the top takes energy, and it comes out of the spin, so the top turns noticeably slower after it inverts. In 1955 the physicist A. R. Del Campo pointed out that this alone proves friction is involved. Slowing the spin about the vertical axis needs a torque about that axis, and gravity and the table’s upward push both act straight up and down, so they can’t supply it. Only friction at the contact point can. On a perfectly slippery surface, the trick wouldn’t work, and many tippe tops have a ridged stem to give friction a better grip for the last step.

The full mathematics is stubborn. A key piece is a quantity described by John Hewitt Jellett of Trinity College Dublin in his 1872 Treatise on the Theory of Friction, which combines the top’s rotation with the position of the contact point and stays nearly constant while everything else changes. Researchers were still publishing on how best to model the top’s contact friction in the 2000s, and it turned up as a theory problem at the 2019 Asian Physics Olympiad.

The egg that stands on end

You probably have a tippe top in your fridge. If you lay a hard-boiled egg on its side on a smooth table and spin it hard, it will rise up and spin on one end, just like the top climbing onto its stem. A raw egg won’t do it.

For more than a century, that was a party trick with no complete explanation. Then on March 28, 2002, just before Easter, the Cambridge mathematician Keith Moffatt and the Japanese physicist Yutaka Shimomura of Keio University published a short paper in Nature called “Spinning eggs — a paradox resolved.” Moffatt is the same researcher whose 2000 paper on the finite-time singularity of Euler’s Disk turned that desk toy into a research topic. The University of Cambridge said the pair had spent six months of their spare time on the egg.

Their answer was friction again, specifically the weak friction from the egg slipping slightly where it touches the table. “If we spin a hard-boiled egg on its side, it mysteriously rises to spin on one end,” Shimomura explained in the university’s announcement. “This is because when a cooked — or solid chocolate — egg spins, it slips a little, producing a frictional force between the shell and surface. This force destabilises the spinning egg and kick-starts it to rise, raising the egg’s centre of gravity.”

The paper showed that if friction vanishes, or if the egg rolls without slipping at all, the rise doesn’t happen. It also extended Jellett’s constant, previously worked out for part-spherical bodies like the tippe top, to any fast-spinning body of revolution, so the same reasoning covers eggs, tops and spheroids. A flattened spheroid spun upright does the reverse of the egg and rises onto its rounded edge.

The raw egg fails because of its insides. The motion you give the shell has to spread into the liquid white and yolk, and that wastes most of the energy, leaving too little spin for the egg to rise. The same difference gives a quick kitchen test, described by San Francisco’s Exploratorium. Spin a raw egg and a cooked egg, touch each one just long enough to stop it, and let go. The cooked egg stays still. The raw egg starts turning again, because the liquid inside never stopped moving. The Exploratorium says a cooked egg needs to be spinning faster than about 10 revolutions per second to stand up.

Moffatt and Shimomura weren’t done. In a 2005 paper in the Proceedings of the Royal Society A, written with Michał Branicki, they showed that a spinning spheroid can do something stranger still while it rises. The table’s upward push on it can oscillate with growing size, and in some cases it falls all the way to zero. When that happens, the egg-shaped body briefly loses contact with the table and jumps.

The rattleback, the stone that prefers one direction

The third toy breaks a different rule. A rattleback looks like a small, shallow canoe, smooth and rounded underneath. Spin it in its favored direction, and it spins smoothly until it slows down. Spin it the other way, and after a turn or two it starts to rock end to end, rattling against the table. The spin dies, and then the rattleback starts turning the opposite way, as if it had changed its mind. Some rattlebacks reverse in either direction, and some will reverse more than once in a single spin.

Its old scientific name is the celt, and that name comes with its own oddity. In a 2008 paper on the toy, Moffatt and the Cambridge mathematician Tadashi Tokieda point out that “celt” is pronounced “selt” and has nothing to do with the Celtic peoples. It’s an archaeologists’ word for a prehistoric stone or bronze tool shaped like a chisel or axe head. Citing the Oxford English Dictionary, they explain that the word came into existence by mistake: some manuscripts of the Latin Vulgate read celte in a verse of the Book of Job where others read certe, “surely,” and antiquaries adopted it around 1700. Popular histories say 19th-century archaeologists noticed that some polished stone celts would spin only one way, which is how the name passed to the toy.

The first person to analyze the celt mathematically was Gilbert Walker, a Cambridge mathematician with a taste for spinning things. He had been top of his year in mathematics in 1889, and his undergraduate interest in boomerangs had earned him the nickname “Boomerang Walker.” In 1895 he described “a curious dynamical property of celts,” and in 1896 he followed with a fuller paper, “On a dynamical top.” Walker later went to India to forecast the monsoons, where he discovered the vast seesaw of air pressure across the Pacific and Indian Oceans that we now call the Southern Oscillation, half of El Niño–Southern Oscillation. The Walker circulation is named after him.

Walker spotted the cause. In a rattleback, the directions in which the body is most and least resistant to turning don’t line up with the directions of its curved bottom. The axes of its mass are slightly twisted relative to the axes of its shape. Usually this is built in by making the bottom slightly skewed, or by adding off-center weights.

That twist couples three motions that would otherwise be independent: the spin, rocking end to end (pitching), and rocking side to side (rolling). You can see the coupling without spinning it at all. Moffatt and Tokieda note that if you tap one end of a celt to make it pitch, it starts spinning in one direction, and if you push on one side to make it roll, it spins in the other direction. When you spin it the “wrong” way, a pitching wobble grows and grows, drawing energy out of the spin until the spin stops. Then the twisted shape turns that rocking back into rotation in the favored direction. Spun the “right” way, the wobble that would develop is weaker, and friction usually wins first.

The rattleback was a quiet curiosity until 1979, when Jearl Walker, a different Walker, wrote about it in his “Amateur Scientist” column in Scientific American. A wave of research followed, including a 1988 study by A. Garcia and M. Hubbard that tested friction and air-resistance models against real rattlebacks. Moffatt and Tokieda later stripped the reversal down to a simple set of three equations. Without friction, those equations predict that a celt would reverse forever, back and forth. Adding a little energy loss lets them reproduce a real celt’s behavior, with any given number of reversals. They called it “the simplest prototype of chiral dynamics” and noted a suggestive parallel with the equations of the dynamos that generate planetary magnetic fields.

Friction is the engine, not just the brake

We usually think of friction as the thing that makes moving objects stop. These toys flip that idea around. In the tippe top and the spinning egg, friction at a single sliding point is what lifts the heavy end into the air. In the rattleback, energy loss from friction decides which direction wins. Euler’s Disk, which screams toward infinity before it stops, is the same family: the interesting part of the story is always how a spinning body gets rid of its energy.

The rattleback’s trick, a small coupling that lets one kind of motion grow at the expense of another, echoes the twisting that tore apart the Tacoma Narrows Bridge in 1940. And friction can do stranger work still: it can make light when you crunch a mint in the dark.

Try it on your kitchen table

You can see two of the three effects without buying anything. Hard-boil an egg, let it cool, and spin it on its side on a smooth, hard table as fast as you can, holding it lightly and twisting with your fingers. It may take a few tries before it rises. Then try the stop-and-release test with a raw egg next to it.

A rattleback is harder to improvise, though a bent spoon can be coaxed into acting like one. If you’d rather have the real things, a solid metal tippe top and a weighted rattleback will each reliably do their tricks on a glass table or a smooth countertop. Just don’t expect them to be easy to explain. Pauli and Bohr couldn’t do it on the spot either.

Further reading