Skip to the content
  • Search
    • Deutsch
    • Leichte Sprache
    • Čeština
  • Font/Contrast
    • Change contrast
    • Enlarge font
  • Exhibition
    • The Exhibits
    • Mobile Adventure Land
    • MathsLive
  • Visit
    • Visitor information
    • Contact
  • Adventureland Online
    • Advanced Texts
    • Workshops2Go
    • #enjoyinglearning
  • Schools visiting
    • Schools visiting
    • Workshops
    • Tips for the visit
  • Leisure
    • Leisure
    • The Epsilon
    • Actionsbounds
    • Mathematics in Conversation
    • Handicraft sheets
    • Borderless Adventure Land
  • About Us
    • About Us
    • Support Association
    • Sponsors and Supporters
    • Jobs
    • Contact
  • Exhibition
    • The Exhibits
    • Mobile Adventure Land
    • MathsLive
  • Visit
    • Visitor information
    • Contact
  • Adventureland Online
    • Advanced Texts
    • Workshops2Go
    • #enjoyinglearning
  • Schools visiting
    • Schools visiting
    • Workshops
    • Tips for the visit
  • Leisure
    • Leisure
    • The Epsilon
    • Actionsbounds
    • Mathematics in Conversation
    • Handicraft sheets
    • Borderless Adventure Land
  • About Us
    • About Us
    • Support Association
    • Sponsors and Supporters
    • Jobs
    • Contact
  • Search
  • Font/Contrast
    • Kontrast ändern
    • Schrift vergrößern
    • Deutsch
    • Leichte Sprache
    • Čeština

Wobble Stone

This stone, quite inconspicuous at first sight, has fascinated people for hundreds of years. It was usually found in riverbeds or by the sea as a round-washed ellipsoidal body that looks symmetrical from the outside but has an inhomogeneous — i.e. not uniform — mass distribution inside. By the way, it doesn’t take much effort to recreate the strange behaviour of this stone. If you have an old spoon at home that you no longer need, you can bend the handle over the ladle so that it balances on the round bottom. Depending on which side it protrudes more, there is a preferred direction of rotation. If you now bring the spoon to rotate on a flat surface, you will see that it comes to a stop in the preferred direction of rotation simply by friction. In the other direction, however, the rotation speed decreases faster and the energy of the rotation leads to a rocking motion. This rocking motion in turn turns into a rotating motion, and in the opposite direction! The spoon has therefore reversed its angular momentum by itself. Celtic diviners used this apparent obstinacy to make decisions or to interpret the will of the gods. Whether this was done out of ignorance or with ulterior motives is not immediately comprehensible to us, because depending on how you ask the question, the stone naturally always gives you the answer you would like to have. But we will see in the following that there is no higher will or cosmic power behind this.

Figure 1: Bent spoon as a “wobble stone”

And now … the mathematics:

Every body with mass has a centre of gravity and its three main axes of inertia pass through it. These are the axles where you could clamp it and rotate it without it “yawing“. In the case of car wheels, for example, the inhomogeneity of the tyres caused by the manufacturing process is subsequently compensated for with small weights. The main axes are always perpendicular to each other and they coincide with the symmetry axes in symmetrical bodies. The axes of the Celtic wobble stone do not lie on top of each other, hence the asymmetry in its movement. Only that rotation around the vertical axis is stable where it “runs ahead” of the horizontal ones. In the other direction, the rotation is unstable. There is some balance, but it is like balancing a football on the tip of a needle. The smallest impact is enough to throw the system out of balance. In the case of the Celtic wobble stone, this impulse is caused by the frictional force at the point of contact. If there were no friction, the rotation would be stable in both directions. What happens now is that the energy of the rotation flows into the rocking movement. From here on, it is now no longer surprising that with each up and down movement, the stone tilts further in the direction on which the additional mass lies. After only a short time, the rotation in the preferred direction of the rocking motion has taken all the energy away and the stone rotates just as if it had been given the rotational impulse in the same direction, only now, of course, the energy that has been “destroyed” by friction in the meantime is missing.

The exact principle of why the stone now behaves this way and not another way is hidden in complicated equations, but it would still be interesting to mention that in the meantime stones have also been made that are unstable in both directions. Depending on how cleverly you apply the weights, the frequency ranges in which the rotation becomes unstable shift. For example, if you turn your spoon very quickly in either direction, nothing happens at all. Only when the rotation frequency comes into the range of the rocking frequency does the asymmetry become noticeable. If you exploit this behaviour, you can build many different frequency ranges into one and the same stone. There are already some that can reverse their angular momentum up to five times. However, these are difficult to produce, as the ground must also be well chosen so that there is still enough rotational energy after the first change of direction.

Literature

Kuyper, F.: Klassische Mechanik, 9. Auflage, Berlin, 2010.

Opening Hours and Ticket Prices

Tuesday – Friday: 9 am – 5 pm
Saturday, Sunday and holidays: 10 am – 6 pm

Entry: 5 Euro / discount. 4 Euro

Special prices apply for groups and families, for guided tours or for photo and video permission.

  • Legal Notes
  • Data protection
  • Accessibility
© 2022

Adress

Erlebnisland Mathematik
Technische Sammlungen Dresden
Junghansstraße 1-3
01277 Dresden

Visitor Service

0351 – 488 7272 | service@museen-dresden.de