Why the humble tippe top baffled physicists and statesmen

Tippe tops flip themselves over when spun. The toy was a physics puzzle that fascinated at least two Nobel Prize Winners and one of the Allies' greatest strategists in World War II.

Tippe tops are round tops that, when spun fast enough, tip sideways and eventually turn upside down so that they are spinning on their thin handles. To do this, the tops have to actually lift their bodies up, off the surface they're spinning on. How does a lateral spinning motion push a top upwards?

This question absorbed several brilliant and famous minds. Niels Bohr, who helped figure out the structure of the atom, and Wolfgang Pauli, best known for the Pauli Exclusion Principle, both famously studied the tippe top to figure out what made it flip itself. Winston Churchill, most famous for helping the Allies win World War II and turning a phrase like nobody's business, also loved the thing.

Why the humble tippe top baffled physicists and statesmen


(Pictured Left: Wolfgang Pauli and Niels Bohr doing what Nobel Prize winners do with their spare time.)

But how does it work?

The most spectacular move the top makes is the jump to its stem. Sometimes it does it so so violently that it hops off the surface it's spinning on. It's eye-catching, but it's just a continuation of what was already happening; friction from the spin pushing the center of mass upwards.

The center of the curve described by the bottom of the top is higher than the center of mass. The curve will pull its center towards the lowest possible point – much the way the curve of an egg, if placed on end, will fall sideways and rest on its flatter side, pulling its center down. Meanwhile, an untethered object, if spun, will rotate around its center of mass. The center of mass has been lifted up and to the side when the top falls sideways.

Usually, when an object spins, the point that it's spinning on – the point of the object that makes contact with the ground - is directly below the object's center of mass. That contact point is steady on the ground and doesn't move. The object spins around it.

When a tippe top spins, because of the switcheroo trick the curve pulls, the point of the object that touches the ground is not below the center of mass. It is below the center of the curve, slightly to the side of the center of mass. The object still must spin around the center of mass, though, so the contact point of the top gets dragged around in a circle. The motion of the spinning top pushes that contact point down and to one side. Anyone who has dragged an object along the ground knows the feel of friction. It counteracts the force one puts on the object. If the spin of the top is pushing the contact point down and to the side, the ground is pushing the top up, and to the opposite side. The top feels a force pushing up and backwards.

Why the humble tippe top baffled physicists and statesmen

The blue dot represents the center of mass, around which the top spins. The yellow dot represents the center of the curve. There is no point of contact with the floor below the center of mass. Because of that, the contact point, below the center of the curve, gets dragged around in a circle.

This force pushes the top's center of gravity even higher and farther to the side. If the top has not been spun hard enough it stops spinning and comes to rest. If the angular momentum it experiences is enough, the momentum keeps driving the point of contact in a wider and wider circle. This results in more force, which pushes the center of mass higher, and the top more onto its side. Eventually the top flips completely.

Via FYSIK, Anirudh.net, and Physik.