Dynamics

Dynamics is the study of forces. From Newton's definition of force we are able' to see the natural divisions of the subject. This definition is as follows: - Force is that which changes or tends to change a body's state of rest or motion. It will be seen that there are four parts to the definition. Two of these lead to Kinetics, and the other two to Statics. The study of forces whose resultant action changes a body's state of rest or motion, is termed Kinetics; the study of forces which in combination only tend to change a body's state of rest or motion, is termed Statics. Many writers use the term Mechanics to include the whole subject, and divide it into the branches Dynamics and Statics, assigning to Dynamics the meaning that has been given above to Kinetics. Strictly speaking, the study of machines should be called Mechanics, which is, therefore, a special branch of Applied Dynamics.

In the case of forces acting on water or other liquids, we speak of the science of Hydrodynamics, with its divisions Hydrokinetics and Hydrostatics. Applied hydrodynamics is usually termed Hydraulics.

In the case of forces acting on air or other gases, the term Aerodynamics may be used, with its branches Aerokinetics and Aerostatics. Applied aerodynamics is usually termed Pneumatics.

Finally, the investigation of the motions of bodies without regard to the forces that may be involved in the production of the motions, is ill the province of Kinematics.

The force-relations with small bodies, whose magnitudes arc negligible when compared with their masses, are usually discussed under the head of Dynamics of a Particle. Those bodies that arc not strained by the forces acting on them, i.e. whose particles do not suffer any change in relative position to each other, are called rigid bodies, and their behaviour under the action of such forces gives us Rigid Dynamics or the Dynamics of Rigid Bodies. Whereas all solids become rigid under the action of sufficiently small forces, none arc capable of remaining so if the stresses applied to them exceed definite limits. Principles obtained from a discussion of these two branches are employed in the extension to the dynamics of strained or discontinuous bodies, concerning which, however, comparatively little is known.

Starting with a consideration of motion itself, apart from any question of what may produce it, we first assign a definition. Motion is change of position. Change of position can only be recognised by comparison with the position of other bodies; this fact is expressed by the statement that we have only cognisance of relative motion. Thus, so far as appearances are concerned, there is no telling whether the earth is rotating round its axis from west to east, or whether the sun, moon, and stars are rotating round the earth from east to west.

If a rigid body move so that each particle in it travels along a straight line parallel to the path of every other particle, it will invariably present the same aspect in any given direction, and is said to have a motion of translation. Such a motion is instanced by the body of a railway-carriage that runs along a straight railroad. If the rigid body moves so that one set of points in a line is constrained to remain fixed, it is said to have a motion of rotation about that lino as axis, ns in the case of a flywheel on a piece of shafting. If it moves in any other way, its motion will at any instant be compounded of translation and rotation, as in the case of a wheel of the above carriage. It rotates about the axle, and the axle is translated bodily onwards.

Now the rate of change of position may be expressed numerically. It is called speed, and we find the average speed of a moving particle during any interval of time by dividing the distance it traverses by the time taken. The simplest Sort of motion is uniform motion in a straight line; in this case wc should obtain the same average speed whatever interval of space or time we happened to select for measurement. If a train travel 200 miles in 5 hours, its average speed is 40 miles per hour. If for this period of 5 hours its speed be uniform, we should obtain the same result - 40 miles per hour - for any second or minute or hour during the whole five hours.

A body may move in a curved path with constant speed. Its velocity is in that case not constant, this conception involving the meignitude, direction, and sense of the motion [Velocity], and whereas the speed is constant because it only involves the magnitude of motion, the velocity varies because the direction of motion varies along the curve. Change of velocity is called acceleration, and is measured by the amount of change of velocity divided by the time taken to effect the change. When this rate of change is uniform, we have a constant acceleration, as in the case of a falling body near the earth's surface.

It is now necessary to come to the causes of change of motion. The whole science of dynamics is based on three laws formulated by Newton. They were not proved by him, nor by anyone else, being results obtained from experience. We find them true experimentally, and assumptions based on them do not lead to false conclusions. They may be thus stated: - 1. Every body continues in its state of rest or of uniform motion in a straight line, except in so far as'it may be compelled by impressed forces to change that state.

2. Change of motion is proportional to the impressed force, and takes place in the direction of the straight line in which the force acts.

3. To every action there is always an equal and. opposite reaction; or the mutual actions of any two bodies are always equal and oppositely directed.

From the first law it is seen that if a body be motionless, or if it possess uniform motion in a straight line, such a state of things is permanent till fresh impressed force acts on it. Hence every impressed force produces an acceleration in the body; accelerations produced by different forces may or may not neutralise one another,- but each being a measure of the effect produced is a measure also of the cause. The second is the law of quantity. It. states that force may be measured by the amount' of motion it gives to a body in a definite time. A standard force will give standard velocity to standard mass in standard time) or, using the centimetre-gramme-second system of units, we say that a force of one dyne will in one second impart a speed of one centimetre per second to a mass of one gramme. The amount of motion in a body is termed its momentum, and is measured by the product of its mass and its velocity. Change of momentum implies the action of force, and the time-rate of change is a measure of the force.

The third law admits of enormous extension, and may be interpreted as an enunciation of the principle of Conservation of Energy (q.v.). Primarily, it states that when two bodies act on one another the force that one exerts on the other is exactly equal to the force that the second exerts on the first. Hence the momentum given to one is equal to the momentum received, by the. other, and there is therefore no change in the momentum by their interaction, though there may be a redistribution of the same.

The dynamical notion of work is the production of motion against resistance, effected by the action of a force through a definite distance. To do work energy must be available, energy being measured by the amount of work it can do. If, therefore, a body possesses energy, and effects motion against resistance, the third law tells us that the resistance is of the same magnitude as the force exerted by the body, and that the energy spent by the acting body is taken in by the resisting body. There is, then, no loss of energy during the interaction, though it may change its form.

Energy may be given to a body by the action of a force thereon. We know that force may be required to change the position of a body; if this change is effected without dissipation of energy in friction, the body will either possess a finite velocity, or else occupy a position from which it will pass with accelerated motion if only it be not subjected to constraint. In the former case the energy it receives is kinetic, and in the latter case potential. [Enebgy.] Anything from which energy may be obtained is called a source of energy, though, strictly speaking, it is never more than a converter of one form of energy into another. The rate at which the supply may be obtained is called the power of that source. Any converter can supply an indefinitely large amount of energy if only sufficient time be given to it; but the more powerful the machine is, the less the time taken to render a given amount of energy available.