Environmental Engineering Reference
In-Depth Information
(a)
(b)
(c)
Figure 2.10
A variant of Newton's rotating bucket.
relative to the infinite set of inertial frames is absolute. Newton used the following
experiment to demonstrate this point. A bucket filled with water is hung from a
ceiling on a long rope. The bucket is slowly rotated many times so that the rope
twists. Once the rope is sufficiently twisted, and any motion of the water has died
away the surface of the water is horizontal as shown in Figure 2.10(a). The bucket
is then released and starts to rotate with increasing angular speed about the axis
of the rope. The water is dragged along by the inner wall of the bucket until the
situation is as shown in Figure 2.10(b), where both the water and the bucket are
rotating in the same sense. Once this state is established we grab hold of the bucket
to stop the rotation and we observe that the water continues to rotate even though
the bucket is stationary as shown in Figure 2.10(c). What can we conclude? The
fact that the surface of the water makes a concave shape in (b) and (c) seems to
imply that the water is accelerating. We might therefore venture to propose that
the water's surface can be used to identify the existence of accelerations. But we
must be careful because the water does not rotate relative to the bucket in (b) yet
it is still pushed up the sides of the bucket. This is because the rotating bucket in
(b) constitutes a non-inertial frame, so what we really mean is that curvature of the
water's surface defines a non-zero acceleration relative to any inertial frame.
If you feel uneasy about the specialness of inertial frames then you are in good
company. The physicist Ernst Mach (1838 - 1916) attempted to eliminate the dis-
tinction between inertial and non-inertial frames by attributing the curvature of the
water's surface in Newton's bucket to an interaction between the water and the
rest of the Universe (Mach's Principle). This interaction is constrained by the fact
that we should not be able to tell the difference between a situation in which the
bucket rotates and the rest of the Universe is fixed, and one in which the bucket
is stationary and the Universe rotates. Inertial frames are then special only in so
far as they are the set of frames in which the force of interaction with the rest of
the Universe just happens to vanish. The obvious question to ask is whether such
a force actually exists. Since it is both additive and operates over large distances,
the prime candidate is the force of gravity. There have been several attempts to
investigate the gravitational forces produced by distant rotating shells of matter and
