There is, however, another sense in which the term "force" is employed, which, in distinction from the above, is termed a statical sense. This "statical force" is the force by the exertion of which a body keeps still. It is the force of inertia--the resistance which all matter opposes to a dynamical force exerted to put it in motion. This is the sense in which the term "force" is employed in the expression "centrifugal force." Is that all? you ask. Yes; that is all.
I must explain to you how it is that a revolving body exerts this resistance to being put in motion, when all the while it is in motion, with, according to our above supposition, a uniform velocity. The first law of motion, so far as we now have occasion to employ it, is that a body, when put in motion, moves in a straight line. This a moving body always does, unless it is acted on by some force, other than its impelling force, which deflects it, or turns it aside, from its direct line of motion. A familiar example of this deflecting force is afforded by the force of gravity, as it acts on a projectile. The projectile, discharged at any angle of elevation, would move on in a straight line forever, but, first, it is constantly retarded by the resistance of the atmosphere, and, second, it is constantly drawn downward, or made to fall, by the attraction of the earth; and so instead of a straight line it describes a curve, known as the trajectory.
Now a revolving body, also, has the same tendency to move in a straight line. It would do so, if it were not continually deflected from this line. Another force is constantly exerted upon it, compelling it, at every successive point of its path, to leave the direct line of motion, and move on a line which is everywhere equally distant from the center to which it is held. If at any point the revolving body could get free, and sometimes it does get free, it would move straight on, in a line tangent to the circle at the point of its liberation. But if it cannot get free, it is compelled to leave each new tangential direction, as soon as it has taken it.
This is illustrated in the above figure. The body, A, is supposed to be revolving in the direction indicated by the arrow, in the circle, A B F G, around the center, O, to which it is held by the cord, O A. At the point, A, it is moving in the tangential direction, A D. It would continue to move in this direction, did not the cord, O A, compel it to move in the arc, A C. Should this cord break at the point, A, the body would move; straight on toward D, with whatever velocity it had.
You perceive now what centrifugal force is. This body is moving in the direction, A D. The centripetal force, exerted through the cord, O A, pulls it aside from this direction of motion. The body resists this deflection, and this resistance is its centrifugal force.
Fig. 1
Centrifugal force is, then, properly defined to be the disposition of a revolving body to move in a straight line, and the resistance which such a body opposes to being drawn aside from a straight line of motion. The force which draws the revolving body continually to the center, or the deflecting force, is called the centripetal force, and, aside from the impelling and retarding forces which act in the direction of its motion, the centripetal force is, dynamically speaking, the only force which is exerted on the body.
It is true, the resistance of the body furnishes the measure of the centripetal force. That is, the centripetal force must be exerted in a degree sufficient to overcome this resistance, if the body is to move in the circular path. In this respect, however, this case does not differ from every other case of the exertion of force. Force is always exerted to overcome resistance: otherwise it could not be exerted. And the resistance always furnishes the exact measure of the force. I wish to make it entirely clear, that in the dynamical sense of the term "force," there is no such thing as centrifugal force. The dynamical force, that which produces motion, is the centripetal force, drawing the body continually from the tangential direction, toward the center; and what is termed centrifugal force is merely the resistance which the body opposes to this deflection, precisely like any other resistance to a force.
The centripetal force is exerted on the radial line, as on the line, A O, Fig. 1, at right angles with the direction in which the body is moving; and draws it directly toward the center. It is, therefore, necessary that the resistance to this force shall also be exerted on the same line, in the opposite direction, or directly from the center. But this resistance has not the least power or tendency to produce motion in the direction in which it is exerted, any more than any other resistance has.