Angular Momentum-RattleBacks (Bob Fiero)

^{b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) =�mgh (h is the change in the elevation).}

^{c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.}

d. Students know how to calculate momentum as the product mv.

e. Students know momentum is a separately conserved quantity different from energy.

f. Students know an unbalanced force on an object produces a change in its momentum.

g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.

h. Students know how to solve problems involving conservation of energy in simple systems with various sources of potential energy, such as capacitors and springs.

Questioning Script

Prior knowledge & experience:

A rattleback, also known as an "anagyre", "celt", "Celtic stone", "rattlerock", "spin bar", "wobble stone" or "wobblestone" and by the product names "ARK," "Bizzaro Swirls," "RATTLEBACKS," "Space Pet" and "Space Toy," is a semi-ellipsoidal top which will spin on its axis in a preferred direction. But, if spun in the opposite direction, it becomes unstable, "rattles", stops and reverses its spin to the preferred direction. It is an elliptical shaped piece of plastic that has some unusual properties. Place the Rattleback on a smooth, hard, level surface with the curved side down and tap it gently to make it spin. If you purposely give it a spin in the clockwise direction, it will turn through a few revolutions, stop, rattle or rock up and down on its long axis and then automatically reverse itself and spin gently in the opposite direction.

This spin-reversal motion seems, at first sight, to violate the angular-momentum conservation law of physics. Moreover, for most rattlebacks, the motion will happen when the rattleback is spun in one direction, but not when spun in the other. These two peculiarities make the rattleback a physical curiosity that has excited human imagination since prehistorical times.

Root question:

Why does the rattleback continue to spin in one direction (counter-clockwise) but in the opposite direction (clockwise) it will stop and reverse its spin for significant number of revolutions?

Target response:

Due to its offset centre of gravity, it has a preferred direction of rotation which happens to be counter-clockwise. They have a slight curve that is almost un-noticable. When it turns one way there is a bit of resistance which causes it to wobble and slow. When spun in the direction of the shifted balance it spins freely. "Strictly speaking, it's the kinetic energy contained in the oscillations (rocking) of the rattleback that is transformed into rotational kinetic energy. Angular momentum is conserved because as the rattleback spins, the earth spins a little in the other direction (but a tiny amount), because they are coupled by friction." To sum it up, the shape is not perfect so it wont spin easily one way.

Here is a longer version of the explanation above: The curved bottom is asymmetric (it is curved more on one side than the other). When the rattleback begins to turn in the wrong direction, the motion is unstable and the rattleback wobbles. Because of the shape on the bottom side, the wobbling sets up and then builds a vertical rocking motion. That motion requires energy, which comes from the energy of the rotation, and so the spinning rate decreases. The rocking motion increases until it has all the energy.

But the rocking motion is also unstable because of the shape of the bottom. With each bob up and down, the rattleback effectively falls toward one side rather than straight down. So, it begins to rotate in that direction of fall, which is its preferred direction of spinning. Thus, energy is transferred from the rocking motion to the rotation motion and the rattleback is then rotating as it wants. Throughout this entire process, friction between the bottom surface and the table drains energy from the rattleback, until the rattleback finally slows to a stop.

In the 19th century, stones that (by chance) had the right shape to exhibit the headstrong behavior were known as celts because their behavior was discovered by archaeologists studying the prehistoric axes and adzes they had already called celts. My guess is that a bored researcher happened to idly spin a celt that happened to be shaped to be biased in the spin direction.

Descriptions of the odd behavior and the name celt made their way into 19th century books about rotation but attention to them disappeared until I wrote about this curious physics in the first edition of The Flying Circus of Physics (1975). Later, A. D. Moore of the University of Michigan sent me several of the hundreds of celts that he had fashioned from dental stone. Many mathematically sophisticated articles have been written about them but explaining the details of how the energy is shuffled from rotation to rocking and then back to rotation by instabilities and wobbling is mathematically challenging.

The calculated trajectories of the contact point of the rattle back. The blue represents a torque in one direction due to tipping and the red represents torque in the opposite direction.

Common Misconceptions:

Students will think it defies laws of physics or to be more specific conservation of momentum.

There is shifting liquid inside or it is made of some exotic material as affectedby magnetic fields.

Photographs and Movies

Below is the demo of a professionally made rattleback that you could by as a science toy.