## 12 March 2012

### You can't spin a coin on a rotating spaceship

A story entitled "Flarp Flips a Fiver," by Martin Gardner in the March 1983 issue of Isaac Asimov's Science Fiction Magazine presented two spacemen arguing on a spaceship shaped like a bagel.  Lieutenant Flarp refuses to spin a coin to settle the matter.

Ponder his reasoning, then see the answer beneath the fold...

"Coins won't spin on a rotating spaceship.  The inertial forces of a spinning coin make it behave like a small gyroscope... Because the torus-shaped ship rotates around an axis perpendicular to that of the spinning coin, the coin at once falls over.

Even a flipped coin would behave peculiarly unless its spin axis paralleled that of the ship.  A ballet dancer on such a ship would be unable to execute pirouettes.  Jugglers could not twirl plates on sticks or balls on their fingers.  Yo-yos and tossed Frisbees would act strangely... Devices that rotated around vertical axes (overhead fans, turntables, fly-wheels) would have to be arefully aligned to keep them stable..."
The story then moves on to discuss relative motion vs. absolute motion and whether the inertial field proves the ship is rotating rather than the cosmos.  What is not discussed is whether the size of the spaceship (and thus the rotational speed) is important; I wondered whether the principles involved would apply in a Ringworld.

Embedded image via Wired Science.

1. Do you have a link for the story? Thanks.

1. I don't know whether it's available online; I pulled the issue off my bookshelf.

2. By the same reasoning, coins don't spin on the earth, which is also a rotating reference frame.

The argument does not take into account friction, which causes precession. I can make an argument that a spinning ball or coin will actually correct itself, because the additional contact friction (slightly off axis) should cause a torque that corrects the angular momentum, so that the spinning object stays "up". (Up is defined as towards the center of the space station). I wouldn't trust my intuition that far, but it can't be as simple as "the coin at once falls over".

Besides, if objects acted that peculiarly, then human inner ears would go bonkers, and living in the space station would be unbearable.

1. What's happened here is the failure to distinguish between a large rotating body and a small one.
Ringworld sized objects would feel very difference to smaller systems - the size of a bus, for example. On Ringworld the local direction of travel approximates to a straight line, a coin would have the momentum imparted to it by the ring's rotation and would in effect be in orbit around the sun during its spin. The premise of the Ringworld was that its speed of rotation was considerably above that of the orbital velocity appropriate to its radius, meaning that it has an outwards surface acceleration. In this instance, for small systems acting inside a very large system the effects are very similar to planetary effects that we are familiar with.

Where this falls down is when the scale of the two systems approach each other. If you are 2m tall and are in a rotating system of radius 10m your head is a fifth of the way to the centre and would experience very different accelerations. Particularly the Coriolis forces which would result from your head having 4/5ths of the speed of your feet would mean that if you walked with or against the direction of spin you would fall forwards or backwards almost at once. Axial movement would be fine.
Spinning a coin in this situation would mean the axis of rotation of the coin would very quickly get so far out of line with the local vertical that it would fall over.

2. My knee jerk reaction was nonsense. But then I adjusted my intuition with some reasonable numbers: suppose the space station were some reasonable size, such as the one in the movie 2001. I'd guess the rotating room was something like 20 meters across. Say 19.6 meters diameter

acceleration = r * w^2

if the room has 1g acceleration to mimic gravity then we compute it's spin

a = r

9.8 = 9.8 w^2

rotation period = 6.28 seconds

If we ignore frictional precession the coin should be half way through it's 90 degree fall in 3/4 of the second. That's not instant but it is fast. If the room were smaller then it would be faster.

This is not quite right. as it starts to fall there will be some friction that introduces a precession I think. However in the limit of infinitely fast spin we could ignore that precession and indeed the coin should just rotate sideways

3. For that space station in 2001, with the long, curving-floor corridors, it occurs to me that, if you ran along the corridor opposite to the direction of the station's rotation, you'd get lighter (i.e. the centrifugal effect would be reduced), and if you could run fast enough to cancel out the station's rotation entirely, you could bound into the air and, for a while at least, be weightless and stationary while the walls and floor carry on rotating without you. Of course, the station's air co-rotates with the floor and walls, so the air would nudge you spinward, and you'd soon make contact with the floor, which would probably insist that you match its velocity.

Contrarily, if you had a problem that could be solved with additional apparent gravity -- a particularly stubborn bottle of ketchup, for instance -- you could solve it by running *with* the spin of the station. You just have to watch out for the idiot floating in the middle of the hallway hurtling the other way.

4. Now I have to read Ringworld again. It has been a while since I read it last. For some reason my aging memory thought that Pournelle was involved in writing it, too. Oh, well...can't remember everything.

5. Flipping a coin should work fine. Spinning a coin on a flat surface perpendicular to the direction of gravity (e.g. a table) should work for a little while, but as they point out, will work to keep its axis of spin pointing in the same universal direction. As the table revolves out from under it (from the coin's point of view this is a slow tilting action) the coin will get little pushes from the table on each spin, as it collides slightly.

I think the rotation might be slow enough, though, that the coin would just continually adjust. That's just a gut feeling, though; I don't actually have a good feel for the period of rotation of a space station.