[Physics] How to the Earth keep spinning with a liquid core

angular momentumearthfrictionnewtonian-mechanicsrotational-dynamics

In regards to the 'conservation of angular momentum' being the explanation of why celestial objects spin…

If you fill a ball or any other container with a liquid and try to spin it, you will not see any more than 5 or 6 revolutions because of the frictional losses of the liquid inside the container.

I first discovered this during lunch in grade school when I tried to spin my milk carton by throwing it up into the air while giving it a 'spin'. At best, I could get only 3 rotations out of it. This same principle can be seen when you spin a raw egg and a hard boiled egg on a table top. The cooked 'solid' egg will spin the raw one won't.

Because of my early experiences with milk cartons and eggs, somewhere in the intervening years I found it hard to believe some of the accepted 'facts' about our planet:

So here is my question: If the age of the earth 4.5 BILLION years, how can it be spinning freely in space with a liquid or semi liquid core for that length of time?

Combine the effects of the liquid core with the effects of liquid oceans and a gaseous atmosphere, all of which are creating resistance to rotation, these frictional losses would have stopped any rotation long ago.

If the earth had a solid core, I could understand it…

If the earth was less that 4.5 billion years old I might understand it…

But given the accepted age of 4.5 billion years with a liquid core and a fluid outer shell I say there is a fly in the ointment somewhere!

Best Answer

Your intuition about spinning fluids is wrong for a couple reasons.

  1. Angular momentum is conserved so an isolated system of any shape will keep on spinning unless it has a way to transfer that momentum elsewhere. If you spun in egg levitating in a vacuum it would spin forever.

  2. The more bumps, flaws, or non-spherical features your container has the faster it can transfer the angular momentum of the fluid to the container, and then from the container to the environment. The Earth has these features, but they are very very tiny compared to the overall (spherical and smooth) size of the planet.

  3. Most containers you've spun have probably caused your brain to over-estimate the amount of angular momentum they have when you spin them because you don't get all of the fluid spinning. When you twist a container the momentum gets transfered from the interface between the fluid and the container rather inefficiently. It takes a lot of revolutions to get everything "up to speed". The Earth, besides having been "up to speed" since the beginning, having been consolidated from an already-spinning volume of dust and gas, is also spinning in isolation, per #1 above.

The Exploratorium exhibit in San Francisco has a great demo of a fluid spinning in a spherical container called the Turbulent Orb:

Turbulent Orb (looks like a gas giant planet encased in a glass sphere)

Their description:

The Turbulent Orb is a large polycarbonate sphere full of special, colored, flow-visualization fluid. The sphere is mounted on top of a pedestal and can be spun in either direction and at different speeds. The fluid in the sphere shows swirls and waves of internal fluid motions produced by the actions of the visitors. The turbulence of the fluid in the sphere is reminiscent of the turbulent flows that occur in planetary atmospheres. This exhibit shows the complexities of fluid motion that can be produced by very simple circumstances.

My own experience playing with the exhibit is that you must spin the outer sphere around dozens of revolutions before all of the fluid in it is moving uniformly. Once you do that, the fluid inside of it continues to spin for quite some time. Because the fluid has a pearlescent additive you can even find evidence that the central portion of the fluid keeps spinning faster than the outer fluid (which slows faster due to friction with the stationary shell). If you first spin the orb in one direction and then let the outer fluid slow a bit, and then spin it in the opposite direction you'll see vortices form with axes tangential to the outer sphere. You do not get this effect if you start spinning it when the fluid is stationary.

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