## 04 March 2017

### "Rattleback" explained

Other videos here and here (QI).
A rattleback is a semi-ellipsoidal top which will rotate on its axis in a preferred direction. If spun in the opposite direction, it becomes unstable, "rattles" to a stop and reverses its spin to the preferred direction.

This spin-reversal appears to violate the law of the conservation of angular momentum. Moreover, for most rattlebacks the motion will happen when the rattleback is spun in one direction, but not when spun in the other. Some exceptional rattlebacks will reverse when spun in either direction. This makes the rattleback a physical curiosity that has excited human imagination since prehistorical times.

#### 5 comments:

1. Interesting and little plastic rattlebacks can be had on amazon for a few dollars. Fun.

2. It obviously never stops moving, transfers it's energy to a vertical direction and back to horizontal at a much slower pace in the 'opposite' direction. Am I missing something here??

1. Well both energy and momentum (linear and rotational) are conserved in the universe so the energy solution answers half the mystery. It remains to explain how it transferred its rotational momentum to the table/earth and then how it stole some rotational momentum in the opposite direction from the table/earth.

2. I assumed that it transferred the rotational momentum into rocking momentum and then, because of some left-right asymmetry, when the momentum transferred back to rotation, the rotation was in the opposite direction. (note that when you start by spinning it the other way, nothing unusual happens).

3. So that is a good thought; but energy, linear momentum, and rotational momentum are all conserved independently.

If you take your right hand, stick your thumb out, and curl your fingers in the direction of motion you will find that the way your thumb is pointing aligns with the vector of angular momentum of the object.

The direction of that vector cannot change even one degree without a torque being applied to the object. You have noticed this if you have ever tried to turn a gyroscope spinning flat with the ground 90 degrees on its side. It provides a lot of unexpected resistance and requires a lot of torque to be changed to spin around the new vector.

This is basically a form of newtons first law applied to rotating objects: "an object in rotation stays in rotation with the same speed and about the same axis unless acted upon by a torque."

So transferring the spinning motion to with a "downwards" (i.e. into the table) pointing angular momentum vector into the "rocking" style motion (which would have alternating angular momentum vectors parallel to the table surface) requires that a torque be applied somewhere. Just like turning a gyroscope on its side.

Then another torque is needed from there to change the rocking motion into the reversed spin motion.

So where does this torque come from? I haven't studied the rattleback well enough to know for certain, but there are a pair of videos I found ([1], [2]) that seem to point in the right direction. Both of these videos seek to reduce the friction at the point where the rattleback contacts the surface and when they do the strange reversing behavior disappears (i.e. is not observed).

This leads me to suspect that the friction at the point/area of contact is the source of the torque.