If the earth started spinning clockwise

Flustered

Maybe i'm lost but what is the significance of the rotating book?

Bob S

If the Earth's angular momentum is unchanged, and the Earth's body axis flipped say over in a year (365 revolutions), an observer on Earth would see the east→west direction of the tides change by ~3 degrees per day to west→east. An observer in space would say that the Earth's tides did not change direction, but would say that the north and south poles flipped.

By the way, the vector sum of the Earth's and Moon's angular momentum is conserved. When the Earth's rotation slows due to tidal forces, down, the Moon's angular momentum increases due to tidal forces, and moves to a higher orbit.

Read ".........First there is a real retardation of the Moon's angular rate of orbital motion, due to tidal exchange of angular momentum between the Earth and Moon. This increases the Moon's angular momentum around the Earth (and moves the Moon to a higher orbit with a slower period). Secondly there is an apparent increase in the Moon's angular rate of orbital motion (when measured in terms of mean solar time). This arises from the Earth's loss of angular momentum and the consequent increase in length of day.[8]" in http://en.wikipedia.org/wiki/Tidal_acceleration

Bob S

Watch very carefully when the book is rotating about its intermediate principal moment of inertia axis. Note that the book binding is flipping from the left side to the right side, and back.

Flustered

Yes I observed that, but what does this prove? Did someone think that was impossible?

Bob S

Au contraire. Physicists realized not only that it was possible, but had to occur when a solid body spins about its intermediate moment of inertia axis.........

Flustered

So you are saying that the Earth may go through this flip?

D H

No, it's not. Sans some external torque, angular momentum is a conserved quantity. Your flip ("if the earth started spinning clockwise") does not conserve angular momentum. It would require a huge, huge, huge, external torque.

Your question is essentially one of those "what do the laws of physics say would happen if we found a way to violate the laws of physics" kind of questions.

Bob S

Are you saying that this demonstration on the International Space Station does not conserve angular momentum? http://www.youtube.com/watch?v=GgVpOorcKqc

D H

First off, the top of the book is always turning toward the camera. There is no reversal of the angular velocity vector here.

Secondly, this is a book, an object with three very distinct principal axes. Labeling the principal moments of inertia as A, B, and C, with A<B<C, for this book the ratio of the largest moment of inertia to the smallest, C/A, is about 3. The intermediate unstable axis B has an moment of inertia that is just about ideally placed in terms of maximizing tumble. Compare that to the Earth. The Earth is very close to a symmetric top; the ratio (B-A)/C is very, very tiny. Moreover, the ratio (C-A)/C is about 1/309. The large scale tumbling seen in that video becomes a tiny little thing called the Chandler wobble with the Earth.

Thirdly, this is a book, a rigid body. The Earth is an elasto-plastic body. This makes the behavior deviate from that of a rigid body. The Chandler wobble doesn't have quite the frequency one would expect for a rigid symmetric top. The magnitude of the wobble oscillates, alternately damped and excited by the polar tide.

There is a phenomenon called polar wander, but this does not involve the earth spinning in the opposite direction. Apparent polar wander results from the motion of the tectonic plates. True polar wander results when the mantle changes orientation. The Earth's rotation axis when viewed from an inertial frame doesn't wander. It is the continents, and possibly the mantle, that wander. This is a very slow process, a degree or so per million years. Whether true polar wander ever did occur remains a bit contentious. There are several articles in the scientific literature arguing for various true polar wander events. There are also articles arguing against such events.

Bob S

A necessary (but not sufficient) prerequisite for an Earth pole reversal without changing the angular momentum vector is reducing the moment of inertia about the C (polar) axis by about 3 x 10³⁵ kg-m². This is equivalent to moving about 7.5 x 10¹⁸ metric tons (7.5 x 10⁹ cubic km) of water from the equator to the poles as an ice cap. Considering that 2 polar caps, each with a thickness of 1 km and a radius of 1000 km is only 6.3 x 10⁶ cubic km, such a scenario is extremely unlikely.

mfb

Probably a differential equation, where the coefficients come from observation of the tides or maybe a simulation of the sea system on earth.

If earth would spin the other way round (ignore the origin of that for a moment), both would slow down at the same time (in case of the moon, it comes closer to earth and gets a higher velocity, but lower angular momentum).

There are some moons in the solar system which orbit in the "wrong" direction. But they are usually small, in irregular orbits and probably captured asteroids.

D H

That's a bit high. You rounded up, you forgot that increasing the C (polar) moment of inertia necessarily decreases at least one of the other two moments, and you used ice rather than rock. There are signs that the Earth has undergone significant true polar wander.

As a starter,

Joseph L. Kirschvink, Robert L. Ripperdan and David A. Evans, Evidence for a Large-Scale Reorganization of Early Cambrian Continental Masses by Inertial Interchange True Polar Wander, Science 277:5325 pp 541-545 (1997), doi: 10.1126/science.277.5325.541
http://web.gps.caltech.edu/~jkirschvink/pdfs/iitpw.pdf

Bob S

Thank you. From your reference:

A variant of this mechanism, inertial interchange true polar wander (IITPW), involves discrete bursts of TPW of up to 90° in geologically short intervals of time if the magnitudes of the intermediate (I_int) and maximum (I_max) moments of inertia cross (36). This would result in a rapid movement away from the spin axis by the geographic location of the former pole with rotation of the entire solid Earth centered about the minimum moment of inertia (I_min) located on the equator. Because I_max, I_int, and I_min are orthogonal, the simple interchange case (with no independent plate motions) yields a 90° shift. Although such an event has not yet been recognized in the geologic record, the geodynamic consequences of an inertial interchange event have been considered in qualitative terms(36). These analyses predict that the 90° rotation of an IITPW event should happen over an interval of 10 to 15 My.

So maybe an interhange of moments of inertia did cause the Earth to spin about an axis that was somewhere near the present equator.