Tippe Toppe Physics

[lincolnrick]

Poking around the 'net today and came across this interesting article about the humble tippe-top

http://io9.com/5689842/why-the-humble-tippe-top-baffled-physicists-and-statesmen

[hemingsoft]

I may have to look back at my old files, but I have had papers about the physics involved in tippy-tops. A popular calculation is the energy minimization as a function of stem angle. Surprisingly, there are also studies of fractal dimensions in tippy-tops!

[poptop]

kids <3 tippe toppes...

[ta0]

The Tippe top, together with the Levitron, is the most amazing spintop around. I have read a few articles about it but I don't have a good intuitive explanation I can share (or that convinces me). I think something perhaps even more amazing that the flipping action is the little known fact that the spin inverts: if you draw an arrow showing the direction in which it is started, at the end is spinning against the arrow (it has to or the momentum would not be conserved)! That means that at some point the top completely stops rotating around the stem axis! By the way, the explanation of the article above is somewhat confusing and I believe not completely correct.

My favorite tipped tops are Toycrafter's. I have several others in plastic, wood and even metal, but none is as good as the old Toycrafter's.

With Takeshi we played with both tippe tops (he took a Toycrafter tippe top with him) and the Levitron. We started the levitron Tuesday night and was still spinning and floating the next morning (of course, I do have the Perpetuator).

[Dick Stohr]

Thanks Jorge, I was thinking about how to say that the top changes direction during the flip. You said it much better that I would have. It just does not make sense, but that is what it does.

[hemingsoft]

The reverse spin reminds me of the demo you showed, ta0, with inducing spin with the magnets in the top. The spin is opposite in that demo too. It clearly shows that the earth has to exert a force on the top such that the spin changes.

Tippy-tops are great examples of stable and meta-stable states and interestingly have great angular momentum dependence on the existence of the stability.

[the Earl of Whirl]

Flip over tops sure are amazing. And I agree that Don Olney and the Toycrafter company had the best flipovers!

[ta0]

The reverse spin reminds me of the demo you showed, ta0, with inducing spin with the magnets in the top. The spin is opposite in that demo too. It clearly shows that the earth has to exert a force on the top such that the spin changes.

Yes, the torque exerted by the earth is not obvious at first on either one. While the inversion of the spin on the induction top reverses the momentum, in the tippe top the momentum does not invert with the inversion of the spin because the top flips over. But no doubt there is an external torque that decreases the momentum as the top uses some of the initial energy to raise the center of mass and therefore has to be spinning slower after flipping.

[samb]

This is an old thread, but it's a topic I found interesting.

First patented in 1891 in Germany, the motion of this top was not properly understood until sixty years later. The inverting top was made famous as it attracted the attention of great minds like Niels Bohr, the Danish physicist who contributed to our understanding of the atom. It captured the world’s imagination throughout the 1950’s when it was mass distributed as a child’s toy. The inverted top is perplexing. When spun, it defies gravity, slowly turning upside down, becoming completely inverted. That’s exciting to watch! But this top performs an even stranger, more subtle trick. As the top inverts, the direction of rotation inverts. Spin the top right side up in a counterclockwise direction, and it will stabilize upside down spinning clockwise! Bohr wasn’t the first to ponder the motion of this curious top, the phenomenon was first discovered by watching children spinning local fruit in South America. Still, no one has more simply explained the counterintuitive motion than A. R. Del Campo. As the inverting top raises its center of mass against the force of gravity, the energy required to do the work must be obtained by a reduction of angular momentum. Therefore the top must spin slower after inversion. The reduction of angular momentum is only possible by an applied external torque. And only the force of friction is present to apply the torque.

The inverting top works because the center of mass is below the geometrical center of the sphere that forms the lower body of the top. Since the rotational axis must go through the center of mass, and the top must rotate about a point (Directly below the axis of symmetry) offset from the center of mass. As the top spins the force of friction acts against the offset, creating the torque which drives the stem down from the vertical and towards the ground. The stem will continue down from its initial vertical orientation until it becomes horizontal. Once there, the rotation about the stem fully stops. As the stem continues to be pulled downward the rotation through the stem starts up again, this time in the opposite direction, so that angular momentum maintains the same direction. Finally the top is drawn up on its stem by the torque generated by the force of friction. It has been transformed, spinning upside down and backwards, albeit a little be more slowly, as the rotational energy was consumed to raise the top upside down.

[the Earl of Whirl]

Don "The Toycrafter" Olney was certainly a dreamer about spinning. I see it more and more every time I go through his collection. He worked quite a long time to understand and make consistent flip over tops out of wood. Once he had it, he found out it was his best seller. He says he easily sold over a million of them. He made them with all kinds of phrases, advertisements and sport logos on them. People were always fascinated with them but not so much the peg top!!!

[ta0]

samb, you may want to also look at his thread: Curious Tippe Top behavior (more!)

[Pepe]

Im still in shock!

[samb]

samb, you may want to also look at his thread: Curious Tippe Top behavior (more!)

Thanks Ta0! I loved the videos!

[Jeremy McCreary]

The inverting top works because the center of mass is below the geometrical center of the sphere that forms the lower body of the top. Since the rotational axis must go through the center of mass, and the top must rotate about a point (Directly below the axis of symmetry) offset from the center of mass. As the top spins the force of friction acts against the offset...

Excellent write-up! The envisioned friction force presumably acts on the contact patch where the top meets the table. But in what direction? Due to slipping, rolling, or some of both?

[ta0]

I suggest you also look at this thread: Turning a Tippe Top
The video mentioned there of Professor Tadashi Tokieda is worth watching (although I'm not completely convinced by his calculation).