(202.) Since the whole pressure is in this case excited on a single
point, the stability of the axis will not be disturbed, provided that
point alone be fixed. So that even though the axis should be free to
turn on that point, no motion will ensue as long as no external forces
act upon the body.
(203.) If the axis of rotation be not a principal axis, the centrifugal
forces will produce an effect which cannot be represented by a single
force. The effect may be understood by conceiving two forces to act
on _different points_ of the axis at right angles to it and to each
other. The quantities of these pressures and their directions depend
on the figure and density of the mass and the position of the axis,
in a manner which cannot be explained without the aid of mathematical
language and principles.
(204.) The effects upon the axis which have been now explained are
those which arise from the motion of rotation, from whatever cause that
motion may have arisen. The forces which produce that motion, however,
are attended with effects on the axis which still remain to be noticed.
When these forces, whether they be of the nature of instantaneous
actions or continued forces, are entirely resisted by the axis, their
directions must severally be in a plane passing through the axis, or
they must, by the principles of the composition of force [(74.) et
seq.], be mechanically equivalent to forces in that plane. In every
other case the impressed forces _must_ produce motion, and, except in
certain cases, must also produce effects upon the axis.
By the rules for the composition of force it is possible in all cases
to resolve the impressed forces into others which are either in planes
through the axis, or in planes perpendicular to it, or, finally, some
in planes through it, and others in planes perpendicular to it. The
effect of those which are in planes through the axis has been already
explained; and we shall now confine our attention to those impelling
forces which act at right angles to the axis, and which produce motion.
It will be sufficient to consider the effect of a single force at right
angles to the axis; for whatever be the number of forces which act
either simultaneously or successively, the effect of the whole will
be decided by combining their separate effects. The effect which a
single force produces depends on two circumstances, 1. The position of
the axis with respect to the figure and mass of the body, and 2. The
quantity and direction of the force itself.
In general the shock which the axis sustains from the impact may be
represented by two impacts applied to it at different points, one
parallel to the impressed force, and the other perpendicular to it,
but both perpendicular to the axis. There are certain circumstances,
however, under which this effect will be modified.
Public-domain text, read in full here on John Shaqi.
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