accomplished this purpose more effectually than they have done, to minds
by whom it was not already well understood.
Let us suppose a body to be moving in a circular path, around a center
to which it is firmly held; and let us, moreover, suppose the impelling
force, by which the body was put in motion, to have ceased; and, also,
that the body encounters no resistance to its motion. It is then, by our
supposition, moving in its circular path with a uniform velocity,
neither accelerated nor retarded. Under these conditions, what is the
force which is being exerted on this body? Clearly, there is only one
such force, and that is, the force which holds it to the center, and
compels it, in its uniform motion, to maintain a fixed distance from
this center. This is what is termed centripetal force. It is obvious,
that the centripetal force, which holds this revolving body _to_ the
center, is the only force which is being exerted upon it.
Where, then, is the centrifugal force? Why, the fact is, there is not
any such thing. In the dynamical sense of the term "force," the sense in
which this term is always understood in ordinary speech, as something
tending to produce motion, and the direction of which determines the
direction in which motion of a body must take place, there is, I repeat,
no such thing as centrifugal force.
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.