Inertia

“ The resistance that a mass of matter opposes to a change in its position or rate and direction of movement, is called inertia. That it should actively oppose anything has been already pointed out as reason for denying that matter is inert, but inertia is the measure of the reaction of a body when it is acted upon by pressure from any source tending to disturb its condition of either rest or motion. ”

“ LECTURE XVI.
INERTIA.
Inertia.—The Hammer.—The Storing of Energy.—The Fly-wheel.—The Punching Machine.
INERTIA.
523. A body unacted upon by force will continue for ever at rest, or for ever moving uniformly in a straight line. This is asserted by the first law of motion (Art. 485) . It is usual to say that Inertia is a property of all matter, by which it is meant that matter cannot of itself change its state of rest or of motion. Force is accordingly required for this purpose. ”

“ One class of philosophers, recognizing the self-existent character of motion, has exhausted ingenuity in the effort to deduce attraction from it, of course wittingly or unwittingly bringing into co-operation the occult force inertia, to obtain vis viva. Another class would deduce all motion from attraction: while in the attempt to contrive a mechanism to explain resiliency—the most incomprehensible of all in a body without parts—immensely greater complications and difficulties have been introduced. Inertia, so far as I am aware, has always been accepted as an inscrutable fact, or ignored. ”

“ If we consider that rest or motion when once established is the normal state of matter, then the force which causes a change causes a breach of the law of inertia. But if we consider that the liability to be moved, or to have motion stopped by force, is itself a property of matter, then the application of force with such result is merely calling into operation the law of inertia. ”

“ On the other hand, under the influence of the mechanics of his day, which had hardly distinguished between inertia, or the inability of a body to change itself, and resistance or the ability of bodies to oppose one another, he concluded that, as inertia is passive, so is resistance, and refused to recognize that in collision the mutual resistance of moving bodies is a force, or active power, of changing their movements in opposite directions. ”

“ If it be said that the velocity of a body cannot change, if there is no reason for it to change, may we not just as legitimately maintain that the position of a body cannot change, or that the curvature of its path cannot change, without the agency of an external cause? Is, then, the principle of inertia, which is not an à priori truth, an experimental fact? Have there ever been experiments on bodies acted on by no forces? ”

“ So long as these motives were habitual, and their attraction regular, the consequent result might, for convenience, be called movement of inertia, to distinguish it from movement caused by newer or higher attraction; but the greater the bulk to move, the greater must be the force to accelerate or deflect it. ”

“ To this objection I reply that there is in social science, as in Nature, a vis inertia; that is to say, there is a tendency in matter to remain at rest if unmoved by any external agency, and also of persisting to move, after it has once been set in motion. The vis inertia of some bodies is greater than that of others, and depends upon their weight and density. ”

“ There yet remain certain properties or bodies as forces which usually are not conceived as modes of motion. Inertia and rigidity are the two most important. If they are deprived of their occult attributes, all other forces fall into line as modes of motion. Inertia, as defined by Newton, is resistance to deflection of motion, or resistance to acceleration, positive or negative; but when we remember that a body has the internal motion of its parts, and properly conceive that these motions are deflected when the body is accelerated, inertia becomes simple as resistance to deflection. ”

“ Inertia, a passive power, is as death, being passive animation; and inertia enabling a body to act against force, is nothing short of active inertia, or vis inertiæ, which means the force of inability. This monstrous perversion of a natural fundamental principle, and by such high authority, pervades the whole of the established philosophy. It makes the planets, which are but clumps of deadly inert matter, gravitate themselves through space; and makes inert atoms competent to perform attraction on each other wherever they exist. ”

“ We have seen how the rotating parts of the engine can be balanced, but we have not considered the reciprocating parts. To understand this question of balancing we must talk about “inertia forces.” All bodies possess inertia, that is, they resent changes in their state of rest or motion. If a body is moving uniformly it tends to keep on doing so, whereas if it is at rest it tends to remain so. To start the body off from rest, or to stop the body and bring it to rest, requires a force to be exerted, and this force may be called the inertia force. ”

“ I abstract here from the fact that a certain intensity of the consciousness is required for its impulsiveness to be effective in a complete degree. There is an inertia in the motor processes as in all other natural things. In certain individuals, and at certain times (disease, fatigue) , the inertia is unusually great, and we may then have ideas of action which produce no visible act, but discharge themselves into merely nascent dispositions to activity or into emotional expression. The inertia of the motor parts here plays the same rôle as is elsewhere played by antagonistic ideas. ”

“ A. If a body is at rest, inertia is that quality by which it will forever remain so, unless acted upon by some force from without; and if a body is in motion, it will continue on at the same speed, in a straight line, forever, unless it is quickened, retarded, or turned from its path by some other force. ”

“ What we term inertia, or the passiveness of matter, is but the equilibrium of opposing forces; and when this equilibrium is destroyed, as for example in chemical changes, motion and activity become visible, and continue until the equilibrium be restored. ”

“ About two thousand years were yet to elapse before that force was explained as elementary inertia; and even that explanation, let us not forget, merely sufficed to push back the barriers of mystery by one other stage; for even in our day inertia is a statement of fact rather than an explanation.
But however little Anaxagoras could explain the centrifugal force on mechanical principles, the practical powers of that force were sufficiently open to his observation. The mere experiment of throwing a stone from a sling would, to an observing mind, be full of suggestiveness. ”

“ To make it clear that this is really the natural generalization of the law of inertia, I shall beg you to permit me a bit of fiction. The law of inertia, as I have said above, is not imposed upon us a priori; other laws would be quite as compatible with the principle of sufficient reason. If a body is subjected to no force, in lieu of supposing its velocity not to change, it might be supposed that it is its position or else its acceleration which is not to change. ”

“ Yet inherent inertia can only be observed relatively: it makes no difference to me whether I am said to be moving at a great speed or absolutely at rest, if I am not jolted or breathless, and if my felt environment does not change. Inertia, or weight, in so far as it denotes something intrinsic, seems to be but another name for substance or the principle of existence: in so far as it denotes the first law of motion, it seems to be relative to an environment. ”

“ So if a force acts on a planet, it produces a change in velocity that is proportional to the force and in the same direction as the force. His law of inertia is that any body, persists in its state of rest or of uniform motion in a straight line, unless affected by an outside force. ”

“ Let us suppose that the principal axis is that of greatest moment of inertia, and that we have made it coincide with the axle of the instrument. Let us also suppose that the moments of inertia about the other axes are equal, and very little less than that about the axle. Let the top be spun about the axle and then receive a disturbance which causes it to spin about some other axis. The instantaneous axis will not remain at rest either in space or in the body. In space it will describe a right cone, completing a revolution in somewhat less than the time of revolution of the top. ”

“ Inertia Shown in the Inability of Matter to Stop its Motion.—Matter, when once set in motion, has no power to stop itself. If it could stop itself it could not be said to be inert. And as it is inert, it would, when once set in motion, keep on moving forever unless stopped by some force. When a stone falls to the ground, it stops simply because the earth stops it. ”

“ On the other hand, B cannot receive from A less motion than A loses, because then B must be admitted to have the power by its resistance of destroying all the deficiency; a power essentially active, and inconsistent with the quality of inertia.
(57.) If we contemplate the effects of impact, which we have now described, as facts ascertained by experiment (which they may be) , we may take them as further verification of the universality of the quality of inertia. But, on the other hand, we may view them as phenomena which may certainly be predicted from the previous knowledge of that quality ”

“ In imaginative works, especially, much depends upon the quality of mere weight. A stern, material inertia is indispensable. It is like the immobility and the power of resistance of a piece of ordnance, upon which the force and efficacy of the projectile finally depend. ”

“ A collection of mere centers of force can have no inertia. If two bodies are considered as two collections of centers of force, the one attracting the other, there is in this view nothing to limit or determine the velocity with which the one body will approach the other. ”

“ No man of sound common sense could ever have doubted that a pressure or force is requisite to set a body in motion in a given direction and that a contrary pressure is required to stop suddenly a body in motion. Though the law of inertia was first formulated with anything like exactness by Galileo, the facts at the basis of it were known long previously to men of the stamp of Leonardo da Vinci, Rabelais, and others, and were illustrated by them with appropriate experiments. ”

“ A gigantic hammer might force in a nail by the mere weight of the head resting on the nail, but with the help of inertia we drive the nail by blows from a small hammer. We have here inertia aiding in the production of a mechanical power to overcome the considerable resistance which the wood opposes to the entrance of the nail. To drive in the nail usually requires a direct force of some hundreds of pounds, and this we are able conveniently to produce by suddenly checking the velocity of a small moving body.
Fig. ”

“ Inertia.—But this principle of the equality of action and reaction appears also in another way. Not only when we exert force upon bodies at rest, but when, by our exertions, we put them in motion, they react. If we set a large stone in motion, the stone 210 resists; for the operation requires an effort. By increasing the effort, we can increase the effect, that is, the motion produced ”

“ Newton admits the principle of inertia, but considers it an innate passive power, which enables a body to resist against being moved; and when in motion, enables it to resist that which would put it out of motion. ”

“ These corpuscles should therefore possess a double inertia: first their own proper inertia, and then the apparent inertia, due to self-induction, which produces the same effects. They will therefore have a total apparent mass, composed of their real mass and of a fictitious mass of electromagnetic origin. Calculation shows that this fictitious mass varies with the velocity, and that the force of inertia of self-induction is not the same when the velocity of the projectile accelerates or slackens, or when it is deviated ”

“ Physically the force of inertia does not exist. Nature nowhere shows us bodies which are devoid of internal activity. We term those which are not alive inorganic, but not inert. Were gravitation alone common to all molecules, it would suffice to prevent the conception of matter as devoid of force. Nevertheless, mechanics only considers the inertia of bodies. ”

“ This brought the inertia of the reciprocating parts of the engine, at every point in the revolution, into equilibrium with the horizontal component of the centrifugal force of the revolving counterweight. ”

“ Now, we have seen that the mass coefficient of inertia increases with the velocity; should we conclude that the mass coefficient of attraction increases likewise with the velocity and remains proportional to the coefficient of inertia, or, on the contrary, that this coefficient of attraction remains constant? ”

“ To us it appears inconceivable that once it required the profoundest meditation to discover the first law of motion, the inertia, as it is called, of matter, in virtue of which the motion of a body does not change without an external cause ”