The Big Wobble

For this to make sense, you need to see something best demonstrated with a racket-like object — pingpong paddle or such.  However, a paperback book with the pages rubber-banded shut will work.  Spin it like a record on a turn-table and it does what you expect.  Spin it around the handle (or the long axis if you’re using a book) and it does what you expect.  BUT, spin it around the third axis, as if you’re flipping pancakes, and it will freak you out.  It tumbles like crazy.  You can’t spin it around this third axis smoothly.

Why?  It’s a degrees-of-freedom thing.  You believe there are 3 independent degrees of freedom to spin around, but the axis of the spin really has only 2 degrees of freedom to determine direction of spin.  Think of it this way, on a globe a point or pole is determined by just two coordinates, latitude and longitude.  If you try to spin around one of the principle axis, i.e., the biggest or smallest moment of inertia (which are necessarily at right angles) then the energy you put in is stable.  Any other angle, and the energy you put in is split between these two natural, stable spin modes.

If you have a perfect sphere, it doesn’t really matter where you pick your axes, they are all the same.  For anything else, the key thing to understand is that rotation around the high-inertia axis is slower than around the low-inertia axis.  Hence when you flip the racket like you’re flipping pancakes, the two directions in which it can spin go at different speeds, hence the crazy wobble.  That’s the little wobble.  If you don’t understand this yet, try spinning other objects until you do.

Now, on to the Big Wobble.  What is the shape of the Earth?  Not a perfect sphere – it bulges at the equator somewhat.  We are spinning stably around a principle moment of inertia.  Now, what happens if we have a global ice melt that re-arranges the mass?  Floating ice doesn’t matter but glaciers do.  Where would the water go if Greenland or Antarctica sloughed off ice?  Yes, it would make sea levels rise, but what is the distribution of oceans around the planet?  Clearly not centered on Greenland and Antarctica.  The center of mass point (average where the mass would go) is probably somewhere in the south pacific.  Such a global event WOULD change the principle moments of inertia of the globe.

Would we get a wobble since we’d no longer be aligned?  The pole already wobbles some – I would love somebody to do this calculation for us and compare magnitudes.

Would surface effects, tides and such, dissipate the excess rotational energy?  Don’t know, but this sounds like fuel for stormy weather to me.

Would sub-surface effects dissipate the energy?  It’s an established fact that the magnetic poles do not line up with the north star.  There is some evidence for historic changes in the past.

My worry is that Earth is not that rigid and it is likely to adjust itself rather than actually do the Big Wobble dance.  Yes, this means serious earthquakes.

I’m not aware of anybody linking global warming directly to increased earthquake activity.  Sure, there is other stuff going on too, but I would love to see somebody in a University Physics Department somewhere tackle these calculations.  Should we be worried?