Centrifugal force

“ In the popular, but incorrect way of speaking, the balance between the centrifugal and the centripetal force will no longer be maintained: the increase of velocity will give the centrifugal force the advantage, and it will slowly draw the body away from the centre. In reality there is no centrifugal force, the only force acting on the earth in her course round the sun being the sun's attraction upon her, which, however, must keep bending her course from the straight line, if she is to maintain her distance. ”

“ An observer who is sitting eccentrically on the disc is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body . But the observer on the disc may regard his disc as a reference-body which is "at rest"; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. ”

“ THIRD.--We have a coefficient of centrifugal force, by which we are enabled to compute the amount of this resistance of a revolving body to deflection from a direct line of motion in all cases. This is that coefficient. The centrifugal force of a body making one revolution per minute, in a circle of one foot radius, is 0.000341 of the weight of the body. ”

“ Besides heat, light, electricity, and magnetism, there are many other modes of being technically called forces. Centrifugal force is one of them; for, in fact, centrifugal force, in spite of the name, is nothing more than "that quantity of movement which is extinguished by centripetal action in the unit of time."
The force of inertia—vis inertiæ—is another technical or conventional force. For it is plain that inertia cannot act; and thus it is impossible to conceive any true force of inertia. ”

“ And the resistance always furnishes the exact measure of the force. I wish to make it entirely clear, that in the dynamical sense of the term "force," there is no such thing as centrifugal force. The dynamical force, that which produces motion, is the centripetal force, drawing the body continually from the tangential direction, toward the center; and what is termed centrifugal force is merely the resistance which the body opposes to this deflection, precisely like any other resistance to a force.
The centripetal force is exerted on the radial line, as on the line, A O, Fig. ”

“ There is a point where the centrifugal force, or the tendency to fly off from the centre, will counterbalance the centripetal, or the gravitation toward the centre, and beyond that point the latter will be vanquished. It is obvious that no portion of the atmosphere can extend beyond the point where the two influences balance, or are in equilibrium, and the projectile force becomes greater than that of gravitation, or its projection into space would follow. ”

“ In each and every case, wherever the centripetal or centrifugal force acts, the action is direct, because it is caused by a physical medium, which physical medium is in direct contact with each body acted upon, and also fills the space between those bodies. With this view of the centripetal force of Gravitation, our Philosophy is made to agree definitely with our experience, which teaches us beyond contradiction, that no body moves, unless it is either pushed or pulled by a physical medium. ”

“ Hence, the centrifugal forces are in this proportion.
The centrifugal force must also increase as the mass of the body moved increases; for, like attraction, each particle of the moving body is separately and equally affected by it. Hence a double mass, moving at the same distance, and with the same velocity, will have a double force. ”

“ Gaining a rapidly-increasing preponderance as the gravitative force does during the closing stages of concentration, the centrifugal force cannot, in ordinary cases, cause the leaving behind of rings when the mass has become dense. ”

“ It does not need a long argument to demonstrate that bodies in such revolutions as the earth is making have a tendency, by centrifugal force, to throw the heavier elements to the outside, and as this seems to be a universal law in all scientific experiments by man, it seems reasonable to suppose the earth’s centrifugal forces are no exception in their results. ”

“ For when a sun is spinning its mass tends to split up by its own centrifugal force, just as a turning wheel, and the faster the sun spins the greater grows its centrifugal force, the greater its tendency to split. And then at last that rate of spin grows so great, and its centrifugal force is such that its mass can no longer hold together, and fission takes place, the sun dividing into two or three or even more stars, that push apart from each other. ”

“ Such is the theory by which some modern thinkers tried to supplant universal attraction. We need not go far to show the utter absurdity of this rash conception, as the most common phenomena and the most elementary principles of mechanics supply us with abundant proofs of its falsity. Centrifugal force is necessarily perpendicular to the axis of the rotation, and is proportional to the radius of the circle described. Hence its intensity, which is a maximum on the equator of the revolving body, diminishes from the equator to the poles, where it becomes = 0. ”

“ That is the operation or action which the fourth law of centrifugal force expresses. An examination of this same figure (Fig. 2) will show you at once the reason for it in the increasing deflection which the body suffers, as its circle of revolution is contracted. If we take the velocity A' B', double the velocity A B, and transfer it to the smaller circle, we have the velocity A C. But the deflection has been increasing as we have reduced the circle, and now with one half the radius it is twice as great. It has increased in the same ratio in which the angular velocity has increased. ”

“ But I read further that the centrifugal force of a body revolving in any given circle varies as the square of the speed. “Thus a body making 10 revolutions per minute will exert four times as much centrifugal force as will be exerted by the same body making 5 revolutions per minute.” ”

“ Next centrifugal force comes into play, flinging off portions of the rotating masses, which become spheres by virtue of the same law of attraction, and are held in orbits of revolution round the central body by means of a composition between the centrifugal and gravitating forces. ”

“ Hence, in the middle latitudes there is a greater weight of air than at the poles, and this tends to press the lower air to higher latitudes. Centrifugal force, however, balances this pressure, so long as the lower air moves with the velocity of the upper strata; but as the friction of the earth retards its motion and diminishes its centrifugal force, it gradually yields to the pressure of the air above it, and moves toward the poles. Near the polar circles it is again retarded by its increasing centrifugal force, and it returns through the middle regions of the atmosphere. ”

“ The fallacy of this argument is that it speaks as though gravitation and centrifugal force were distinguishable experimentally. It presupposes the distinction that we are challenging. Looking simply at the resultant of gravitation and centrifugal force, which is all that can be observed, neither observer can get rid of the resultant force at all parts of space. Each has to be content with leaving a residuum. The non-rotating observer claims that he has got rid of all the unreal part, leaving a remainder (the usual gravitational field) which he regards as really existing. ”