107. There are other curious consequences which follow from the
properties of the centre of gravity, and we shall conclude by
illustrating one of the most remarkable, which is at the same time of
the utmost importance in machinery.
[Illustration: FIG. 30.]
108. It is generally necessary that a machine should work as steadily
as possible, and that undue vibration and shaking of the framework
should be avoided: this is particularly the case when any parts
of the machine rotate with great velocity, as, if these be heavy,
inconvenient vibration will be produced when the proper adjustments
are not made. The connection between this and the centre of gravity
will be understood by reference to the apparatus represented in the
accompanying figure (Fig. 30). We have here an arrangement consisting
of a large cog wheel C working into a small one B, whereby, when the
handle H is turned, a velocity of rotation can be given to the iron
disk D, which weighs 14 lbs, and is 18" in diameter. This disk being
uniform, and being attached to the axis at its centre, it follows that
its centre of gravity is also the centre of rotation. The wheels are
attached to a stand, which, though massive, is still unconnected with
the floor. By turning the handle I can rotate the disk very rapidly,
even as much as twelve times in a second. Still the stand remains quite
steady, and even the shutter bell attached to it at E is silent.
109. Through one of the holes in the disk D I fasten a small iron
bolt and a few washers, altogether weighing about 1 lb.; that is,
only one-fourteenth of the weight of the disk. When I turn the handle
slowly, the machine works as smoothly as before; but as I increase the
speed up to one revolution every two seconds, the bell begins to ring
violently, and when I increase it still more, the stand quite shakes
about on the floor. What is the reason of this? By adding the bolt, I
slightly altered the position of the centre of gravity of the disk,
but I made no change of the axis about which the disk rotated, and
consequently the disk was not on this occasion turning round its centre
of gravity: this it was which caused the vibration. It is absolutely
necessary that the centre of gravity of any heavy piece, rotating
rapidly about an axis, should lie in the axis of rotation. The amount
of vibration produced by a high velocity may be very considerable, even
when a very small mass is the originating cause.
110. In order that the machine may work smoothly again, it is not
necessary to remove the bolt from the hole. If by any means I bring
back the centre of gravity to the axis, the same end will be attained.
This is very simply effected by placing a second bolt of the same size
at the opposite side of the disk, the two being at equal distances
from the axis; on turning the handle, the machine is seen to work as
smoothly as it did in the first instance.
111. The most common rotating pieces in machines are wheels of various
kinds, and in these the centre of gravity is evidently identical with
the centre of rotation; but if from any cause a wheel, which is to
turn rapidly, has an extra weight attached to one part, this weight
must be counterpoised by one or more on other portions of the wheel, in
order to keep the centre of gravity of the whole in its proper place.
Thus it is that the driving wheels of a locomotive are always weighted
so as to counteract the effect of the crank and restore the centre of
gravity to the axis of rotation. The cause of the vibration will be
understood after the lecture on centrifugal force (Lect. XVII.).
LECTURE V.
_THE FORCE OF FRICTION._
The Nature of Friction.—The Mode of
Experimenting.—Friction is proportional to
the pressure.—A more accurate form of the
Law.—The Coefficient varies with the weights
used.—The Angle of Friction.—Another Law of
Friction.—Concluding Remarks.