Moment of inertia

“ If we see a mass of matter undergo any change, we never seek for the cause of that change in the body itself; we look for some external cause producing it. This inability for voluntary change of state or qualities is a more general principle than inertia. At any given moment of time a body must be in one or other of two states, rest or motion. Inertia, or inactivity, signifies the total absence of power to change this state. A body endued with inertia cannot of itself, and independent of all external influence, commence to move from a state of rest ”

“ Nevertheless, no one would doubt that gravity and inertia do coöperate in the machine, nor should we for a moment hesitate to ascribe to the one or the other of these two forces whatever subordinate effects are only explainable by each respectively. ”

“ Introduction of the force of inertia into the preceding enunciations.
The increase of the quantity of motion projected upon an axis or taken along the trajectory is equal to the impulsion of the projected resultant, or to that of the tangential force. The total impulsion of a force is got by methods of calculation and of experiment analogous to those which relate to work. The increase of the moment of the quantity of motion in relation to any axis is equal to the total moment of the impulsions of the forces during the same interval of time; direct geometrical demonstration of this theorem. ”

“ 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. ”

“ In the first place all matter has the property known as inertia, which we may define as that tendency of matter to remain in a state of rest or to continue at a uniform velocity if in motion. It offers a resistance to any change in the state of either rest or motion whether of amount or direction. ”

“ 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. ”

“ 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. ”

“ 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 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ The heavenly bodies are actually in this condition: they continue to move, not because any new forces are applied to them; but, having been once set in motion, they continue in motion because there is nothing to stop them. This property in bodies to persevere in the state they are actually in,—if at rest, to remain at rest, or, if in motion, to continue in motion,—is called inertia. The inertia of a body (which is measured by the force required to overcome it) is proportioned to the quantity of matter it contains. ”

“ 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. ”

“ 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 ”

“ Even with the particles retarding the motion of the aether, the same will be true if, to counterbalance the increased inertia, suitable forces are caused to act on the aether at all points where the inertia is altered. ”

“ The moving prongs have a momentum, and a change in the momentum opposes a reacting force, the so-called inertia reaction, which is equal to the rate of this change. This was discovered by Galileo over three hundred years ago. We experience the operation of this law every time we bump against a moving object. The Irish sailor who, after describing the accident which made him fall from the mast, assured his friends that it was not the fall which hurt him but the sudden stop, appreciated fully the reacting force due to a rapid change of momentum. ”

“ 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. ”

“ So far as we can explain it at all, we may, perhaps, say that the inertia which the matter composing the wheel shares with all other matter is accentuated by the fact that its whirling particles all tend at successive instants to fly in different directions under stress of centrifugal force. At any given instant each individual particle tending to fly off in a particular direction may be likened to a man pulling at a rope in that direction. ”

“ But there is always inertia. And all things everywhere and all the time tend to remain stock still if they are still, until some force makes them move; and all things that are moving tend to keep on moving at the same speed and in the same direction, until something stops them or turns them in another direction. ”

“ Hence what physicists call “force of inertia” is not a passive resistance proceeding from the inertia of matter, but an active exertion of the molecular powers, and has been so called only because, all other things being equal, its intensity is proportional to the mass of the inert body.160 Evidently, inertia itself cannot resist or check the advance of an impinging body. Nothing but a positive action can do it; for nothing but a positive action can communicate to the advancing body that impetus in the opposite direction which alone is competent to neutralize the impetus of the advance. ”

“ It is the equivalent of mass, or the amount of matter as measured by gravity, and is a fixed quantity; for inertia is as inherent as any other quality, and belongs to the ultimate atoms and every combination of them. It implies the ability to absorb energy, for it requires as much energy to bring a moving body to a standstill as was required to give it its forward motion. ”

“ 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. ”

“ The language sometimes used to explain the property of inertia in popular works, is eminently calculated to mislead the student. The terms resistance and stubbornness to move are faulty in this respect. Inertia implies absolute passiveness, a perfect indifference to rest or motion. It implies as strongly the absence of all resistance to the reception of motion, as it does the absence of all power to move itself. The term vis inertiæ or force of inactivity, so frequently used even by authors pretending to scientific accuracy, is still more reprehensible. ”

“ The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration. ”

“ 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. ”

“ Nothing could move—the inertia of matter itself held it in place until it was too late—everything close to those centers of action simply flared into turgid incandescence and added its contribution to the already hellish whole. ”

“ We get numerous examples of this property of the inertia of bodies in our daily experience. Many of the accidents that befall people in various ways are due to this property of the inertia of matter. A cyclist is riding a machine down-hill, and loses control over his machine, with the result that he runs into a wall, and is killed. Now what has happened? The cyclist has participated in the motion of the machine, with the result that when the machine has been suddenly stopped, the body has been thrown forward owing to the momentum it had acquired. ”

“ Supposing an original state of rest, about to pass into motion in obedience to the disturbing forces, the currents commencing at the centre will follow the lines of most rapidly-decreasing density; seeing that the inertia will be least in those lines. That is to say, there will be a current from the centre towards each pole, along the axis of rotation; and the space thus continually left vacant will be filled by the collapse of matter coming in at right angles to the axis. ”

“ Everybody knows that the characteristic feature of matter is what we call inertia. If matter is at rest, a force is needed to set it in motion. If it is in motion, it needs a force to stop it. It needs one to accelerate the movement and one to alter the direction. This resistance which matter offers to the forces which tend to modify its condition of rest or movement is what we call inertia. But different bodies may offer a different degree of resistance to these forces. If a force is applied to an object, it will give it a certain acceleration. ”

“ Hence it is seen that the idea—almost universal—that inertia, or momentum, necessarily coexists with motion, may have no foundation in fact; its error being further evidenced by our non-perception of their coexistence in the invisible, or molecular motions. In fact, inertia or momentum is only perceived in that single mode of motion which produces the sensation of touch ”