MOMEN'TIIM, or QUANTITY of MOTION, is defined by Newton as proportional to the mass moving, and its velocity, conjointly. If we assume unit of momentum to be that of unit of mass moving with unit of velocity, we shall evidently have, for the momentum of a mass 31, moving with velocity V, the expression MV. And such is the unit gener ally adopted.
It is shown by experiment that, when force produces motion in any body, the momentum produced in one second is proportional to the force—and, in fact, force is measured by the momentum it is capable of producing in unit of time. Thus, the same force, if acting for one second on each of a number of bodies, produces in them velocities which are inversely as their masses. Also when, as in the case of falling bodies, the velocities produced in one second are the same in all, we conclude that the are proportional to the masses; and, in fact, this is the proof that the weight of a body is pro portional to its mass. Again, if different forces act, each for a second, on the seine mass, the velocities produced are proportional to the forces. All these are but different modes of statement of the experimental fact that force is proportional to the momentum it pro duces in unit of time; which forms a part of Newton's second law of motion.
When two masses act on each other, Newton's third law of motion (see MOTION, LAWS OE) shows that the forces they mutually exert are equal and opposite. The momenta produced by these must therefore be equal and opposite. Thus, in attraction or impact of two masses, no momentum is lost; since what is lost by one is gained by the other.
The momentum of a system of bodies can be resolved (as velocity is resolved) into components in any assigned directions, and the mutual forces of the system may be thus likewise resolved. Applying the previous result, we see at once that in any system of mutually acting bodies (such, for instance, as the solar system), no momentum is, on the whole, either gained or lost in any particular direction; it is merely transferred from one part of the system to another.
This fact, called the conservation of momentum, has caused great confusion in the minds of pseudo-physicists, who constantly confound it with conservation of work or energy, a totally different thing.
The momentum produced by force in any period of aim is measured by the product of the force and the time during which it has acted—the energy or work done by a force is measured by the product of the force and the space through which it has acted. Momentum is proportional to the simple velocity of a body, and can never, by any known process, be transformed into anything else. Energy, when depending on velocity (see FoncE, CONSERVATION OF), is proportional to the square of the velocity, and is in the natural world constantly being transformed from its actual or kinetic form to its potential form, and back again, or to other kinetic fomn, such as heat, and finally must become heat, Momentum, on the Contrary, is never altered, either in kind or in amount.
In knocking down a wall, or in staving in the whole side of a ship, the battering-ram of the ancients (when constructed of sufficient mass, and worked by the proper number of men or animals) was probably nearly as effective as the best modern artillery. But in making a breach in a wall, or in punching a hole in the armor of an iron-clad, mere mas sive shot with low velocities (such as those of the Dahlgren guns), are comparatively ineffective, however great their momentum; while an Armstrong or Whitworth project ile, with a fraction of the momentum, but with greater velocity, and, for its size, much greater kinetic energy, effects the object with ease.
In many every-day phenomena, we sec most distinctly the difference between these two affections of matter. Thus, a blow delivered from the shoulder by a heavy pugilist, even it it be sluggishly given, generally floors its man, without doing much other injury; but a sharp stroke administered by a light weight, while hardly disturbing the adver sary's equilibrium, inflicts serious punishment.