Page 566 : DYNAMICS — DYNAMICS
Individual articles:
Algoma East in 1904. Is Honorary Lieutenant-Colonel of the 97th Regiment in 1907. A Liberal.
Dynam′ics is that science whose aim it is to describe most completely and most simply the motions which occur in nature. This is the definition given by Kirchhoff. But his illustrious colleague, Helmholtz, defines dynamics as the science of those phenomena in nature which may be reduced to the motion of ponderable masses. The difference between the two definitions is slight; and it vanishes completely if we assume that all the phenomena of nature can be explained, ultimately, in terms of matter in motion.
Perhaps the simplest method of getting a clear idea of the object and the method of dynamics is to consider the orderly sequence of steps by which this science, in its modern form, has been built up.
KINEMATICS
1. Before the motion of a particle can be described, we must be able to define the position of that particle: for motion is merely change of position. For this purpose dynamics mates use of the ordinary geometry of position. As is well known to everyone, when we wish to locate a point on the earth’s surface, we must tell three things about it, namely, its latitude, its longitude and its height above the sea-level. So in dynamics it requires always three specifications (called co-ordinates) to locate a particle. Knowing how to locate points, one can then easily locate any rigid body. For if any three points (not in the same straight line) in such a body are fixed, the entire body itself is fixed.
2. The second step in dynamics is to describe the change of position or displacement in bodies. But since change of position is the same kind of quantity as position itself, we still use simply the geometry of position for this purpose.
3. The third step is to describe the rate of change of position. This introduces a new quantity, time. To measure time we use a body in uniform motion, that is, we use a body which is set in motion and let alone. The most uniform motion that we know anything about is the rotation of the earth on its axis. Accordingly the average period of rotation of the earth with respect to the sun is called a day. And 1-864,00th part of a day is called a second. This is the unit of time most frequently employed in dynamics. The idea of time being clear, the rate of motion or the velocity of a particle is defined as “the ratio of the change of position to the time occupied in this change.” The numerical value of any velocity, without reference to its direction, is called its speed.
4. But since practically all velocities in nature are changing, the fourth step in dynamics is to define the rate of change of velocity. This is called acceleration, and is measured by the ratio of the change in velocity to the time occupied in the change.
Up to this point we have considered merely the motion of a body, but have not asked any questions concerning the causes of these motions. This science of motion alone is called kinematics, which is merely a Greek word for science of motion. Kinematics may be taken as a purely mathematical subject; but, as a matter of fact, it nearly always forms the first chapter of any treatise on dynamics.
DYNAMICS
5. Passing now to the thing in motion—that which we call matter—we find that the quantity of it can be measured just as it was in the case of time and space; but we cannot define it, any more than we could time or space. Time may be called duration and space may be called extension; but no one is any the wiser for all that. So the amount of matter in a body is called its mass; but this is not a definition of matter; it is merely a convenient name for the amount of substance in any body. The measure which is employed for matter is its inertia, that is, its tendency to remain at rest if it is at rest or to remain in motion if it be in motion. If one body is twice as hard to set in motion as another, it is said to have twice the inertia of the other, that is, twice the mass of the other. It was shown by Newton that all bodies, regardless of their chemical composition, are attracted by the earth with forces which are strictly proportional to their masses. And hence we use the balance when we wish to compare (i. e., to measure) two masses.
These three ideas, mass, space and time, are the fundamental concepts of dynamics. Proceeding from these, Galileo, Huygens, Newton and Lavoisier constructed what might be called the first modern system of dynamics. The experimental facts which lie at the foundation of this system are Newton’s laws of motion and Lavoisier’s discovery of the conservation of matter.
NEWTON’S LAWS OF MOTION
Before these experimental facts can be stated in a clear and definite manner, it is essential to introduce two more fundamental quantities, viz., the linear momentum of any body, which is defined as the product of its mass by its velocity, and the force acting upon any body, which is defined as the product of its mass by its acceleration; or, what amounts to the same thing, the time-rate at which the linear momentum is changed. Newton’s laws may now be stated as follows:
I. If a body is in translation under no external force, its linear momentum remains constant.
