Tidal waves, in order to be effective in reducing the rotational speed of a planet, must be accompanied by internal friction; and this requires that the planet be to some extent inelastic.
Laplace assumed a nebula whose form was a function of its rotational speed, its gravitation, its internal heat, and, although he does not so state, of its internal friction.
To illustrate, the rotational velocity of a particle now in the Sun's surface at the equator is approximately 2 km.
Slipher has recently measured the rotationalspeed of one "spindle" nebula, believed to be a spiral.
Further contraction of the planetary masses would give rise to increasing rotational speeds in the west to east direction.
The rotational movement of the earth is becoming gradually slower on account of tidal influence; our day, in fact, becomes an hour longer every few million years.
At the same time the tidal influence of the earth was lessening the rotational movement of the moon.
Apparently, then, the dancer differs radically from most mammals in that it lacks visual and rotational dizziness.
So small was the mass of the moon and so near was it to the earth, that its relative rotational energy was in time completely used up, and the moon has ever since turned her constant face toward us.
Darwin shows that the gravitative interaction of the two bodies immediately began to raise tides of extraordinary height in both, therefore tending to slow down the rotational periods of both bodies.
However, mutual tides of phenomenal height in their early plastic substances must have been a necessary consequence of the action of the Newtonian law, and they gradually drew upon the earth's rotational moment of momentum.
How can one who is ignorant of the existence and characteristics of rotational inertia understand a galvanometer?
Searching problems and discussion are instigated at once, and the notion of rotational equilibrium and force moments brought in.
Quantitative experiments are furnished by the rotational counterpart of the Atwood machine.
By this time the student should have found himself sufficiently prepared to take up problems of rotational motion.
Rotational motion leads naturally to a discussion of centripetal force, and this in turn is simple harmonic motion.
Roughly, the Inertia or Mass of a body expresses its resistance to change of mere translational velocity, whereas, the Moment of Inertia of a body expresses its resistance to change of rotational velocity.
It would be an interesting experiment to measure with a delicate chemical balance the force with which the axis raises itself, and in this way weigh the rotational motion of the earth.
Py dPz dPz dPx dPx dPy vanish, rotational if any one of them is different from zero.
Whether the strain is rotational or not, there is always one set of three linear elements issuing from any point which cut each other at right angles both before and after strain.
A rotational strain can always be analysed into an irrotational strain (or "pure" strain) followed by a rotation.
Stokes afterwards showed that the quicker wave is a wave of irrotational dilatation, and the slower wave is a wave of rotational distortion accompanied by no change of volume.
The energy then, originally drawn from the rotational energy of the earth, has thus worked through the pendulum machine, and is now stored in the air masses in this form of energy of position.
At the outset, it may be pointed out that this energy, applied by hand, is obtained from the original rotational energy of the earth by certain definite energy processes.
In this machine, therefore, the energy of position possessed by the air masses is, in their descent to their original positions at lower levels, transformed once more into axial or rotational energy.
To make the process complete and cyclical this energy must now, therefore, be returned once more to the earth in its original rotational form.
This electric strain is certainly not of the nature of a compression in the ether, but much more akin to a twist or rotational strain in a solid body.
We postulate, therefore, the following ideas: We have to think of the ether as a homogeneous medium in which a strain of some kind, most probably of a rotational type, is possible.
If he is correct, the figure of bifurcation is a limit of stable figures, and none can exist with stability for greater rotational momentum.
Mathematicians are accustomed to regard the density as constant and the rotational momentum as increasing.
He then supposes the liquid forming the cylinder to shrink in diameter, just as we have done, and finds that the speed of rotation must increase so as to keep up the constancy of the rotational momentum.
Poincare discovered, has less rotational momentum than that of the figure of bifurcation.
When the satellite moves in an ellipse of any given degree of eccentricity, there is a certain amount of rotation in the system, technically called rotational momentum, and it is always the same at every part of the orbit.
Hitherto the rotational momentum has been kept up to its constant value partly by greater speed of rotation and partly by a symmetrical bulging of the equator.
A figure titled "A 'family' of elliptic orbits with constant rotational momentum" (Fig.
Hence in order to keep up the rotational momentum, which as we have seen must remain constant, the mass must rotate quicker.
We have then a planetary spheroid, rotating slowly, slightly flattened at the poles, with a high degree of stability, and possessing a certain amount of rotational momentum.
Moment of momentum or rotational momentum is measured by the momentum of the satellite multiplied by the perpendicular from the planet on to the direction of the path of the satellite at any instant.
Footnote 928: The combination of a uniform rotational with an unequal orbital movement causes a slight swaying of the moon's globe, now east, now west, by which we are able to see round the edges of the averted hemisphere.
Their rotational velocity being thus relatively small, they formed "inner rings," very much nearer to the centre of condensation than would have been possible on the unmodified theory of Laplace.
Its orbital momentum, however, is so extremely small in proportion to the rotational momentum of Mars, that any perceptible inroad upon the latter is attended by a lavish and ruinous expenditure of the former.
These were necessary to ensure reasonably uniform rotational speed, as, in addition to having only one cylinder, the governing was of the hit-and-miss type.
Further, that this nebulous matter gradually condensed, and as it condensed, a rotational motion was imparted to them, which rotation quickened as the condensation was continued.
Thus the light wave is always spherical in form, or nearly so, as the rotational and orbital motion of the sun affect the exact shape of the aetherial envelope as we shall learn more fully later on.
What, then, is the effect of the rotationalvelocity of the surface of the earth on the atmosphere near to it?
Further, it is a familiar fact that the shape of all asteroids, satellites, planets, and even the sun is spherical or that of an oblate spheroid, which latter is simply due to its rotational velocity on its axis.
Larmor attributes elasticity to his electrons, such elasticity being of a rotational type.
In ancient days we may indeed suppose that Jupiter being hotter was larger than at present, and that he had considerably more rotational moment of momentum.
In a similar manner we find the rotational moment of momentum for each of the other planets.
Even when the whole of Jupiter's rotational moment of momentum and that of his satellites has become absorbed into the orbital motion, there will hardly be an appreciable difference in the latter.
The rotational contributions of all the planets and of their satellites is very much less, being not more than one sixty-thousandth part of the whole.
Yet even if 1,200 units of rotational momentum had been transferred to the orbital motion it would only correspond with the most trivial difference in the distance of Jupiter from the sun.
With the modern rotational device shown in the diagram, a very narrow beam is aimed at the patient while the source is mounted upon a carrier that revolves completely around him.
Speaking in round numbers, the revolutional moment of momentum of Jupiter is about thirty times as great as the rotational moment of momentum at present possessed by the sun.
On this scale the rotational share which has fallen to our earth and moon does not even rise to the dignity of a single pound, it can only be represented by the very modest figure of 19s.
The gradual increase of the moon's distance could be provided for by a transfer of moment of momentum from two sources, due of course to the rotational velocities of the two bodies.
At present the rotational moment of momentum of the earth is about a fifth part of the revolutional moment of momentum of the moon.
That means, of course, that the velocity of the earth rotating on its axis must be increased, and this again would necessitate an increase in the earth's rotational energy.
Now in the solar system at present, the orbital moment of momentum of Jupiter is nearly fifty thousand times as great as his present store of rotational moment of momentum.
The total, however, of the rotational moment of momentum of the system barely reaches two per cent.
We may, however, assert that so long as the dance is in full swing the total quantity of spin, partly rotational and partly orbital, will remain constant.
