MOMENT. The moment of a force with respect to a point or line about which it tends to produce rotation, is " the product of the force and the perpendicular drawn from the point or line upon the direction of the force. If r be the force, and p the perpendicular, the moment of P is x p.
310.11ENT13f , or 3103fENT. This word has been used in various Remise. It simply means a motion, the word mown, from morimen, being found in several ancient authors. Momentum was originally one rapid motion, whence it came to be used for a very short time ; whence our word consent, which, in common life, means an indivisilSle instant of time. Thus an effect which requires a single second to produce it would not be properly momentary. But the word has passed into mechanics in its original sense of motion, and is used to signify the amount of an effect of motion, actual or conceivable. Thus we have one use in the article VIRTUAL VELOCITIES, another in LEVER, a third in MOMENTUM OP INERTIA, and a fourth, the most common of all, which we proceed to explain in this article.
The English synonym of this fourth sense is "quantity of motion," and we may observe that in this sense it is most usual, in our language, to adopt the Latin form momentum, instead of the abbreviation moment. It is impossible to give an actual definition of momentum, in simple terms : hut the conception is obtained by those who observe that the effects produced by matter in motion (both notions are necessary) may be augmented either by giving the same motion to more matter, or greater motion to the same matter. Imagine a BALLISTIC PENDULUM, and suppose a bullet of two pounds weight to strike it with a velocity of 100 feet per second. The RAMC oscillation which is thus produced, may, it is found, be produced by a bullet of one pound weight striking with a velocity of 200 feet. The same effect being produced in both MACS, though by different quantities of matter and different velocities, there is something which we may assert to be unaltered by the substi tution of the smaller bullet with the larger velocity. This something is the momentum, or quantity of motion, a notion of a cause which is asserted to be the same when effects are the same. This mere defi
nition would be useless except iu connection with principles observed or deduced, by which it may be applied. That there is a reality in connection with it, all who know the difference between light and heavy, as these words are frequently used, are well aware. A heavy blow, for instance, does not mean a blow with a heavy body : thus the fall of a poker may give a light blow, while that of a book of one-tenth part of its weight may give a heavy one. The difference in those map is that of momentum.
The velocity remaining the same, the momentum or quantity of motion increases with the mass moved ; and the mass remaining the same, the momentum increases proportionally to the velocity corn inunicateeL But the peculiar proposition on which the utility of the term and the notion depends la this, that in all mechanical effects produced by matter in motion, a diminution of the mass may be com pensated by a proportionate increase of the velocity : that is, st being the number of unite of mass, and v of velocity, as long as the product of m and v remain," the same, the effect produced is the same. Thus in the preceding instance M x v is 2 x 100 in the first case, and 1 x 200 in the second. And as long as m x v=200, the same effect will be produced.
This product. mv, Is the measure of the momentum, and is generally called the momentum Itself. Hero (as in 3Iasis) tacit reference is made to a unit of momentum : the equation Momentum of m with velocity vs--mxv Implies that a unit of momentum is that produced by a unit of mass moving with a unit of velocity.
When the body moves under the action of a continually applied force, Its is now often expressed by the term dynamical (Ted, by which we mean the effect of a force with reference to its time of action. Thus if a force of 1 1h., acting for one second, produce a certain dynamical effect which we may assume to be unity : then the dynamical effect produced by r lbs. acting for e seconds will be mt. .gow let w be the weight of the body : M its mass : v its velocity : f the rate of acceleration due to r [ird Law of Motion]. Then r : Nemf: hence r.f. f; hence dynamical effect= [.€= fe= mv.
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