Global Positioning System Reference
In-Depth Information
FIGURE A3.
Conceptual
model of a gyrocompass.
The axis
AB
is constrained to
lie in a horizontal plane be-
cause the axis
E
is vertical—
that is, it is pointing to the
center of the earth. The gyro-
scope spin axis is
CD
. A
heavy case weights the gyro-
scope so that if no torque
acts, the spin axis is
horizontal.
horizontal plane. Imagine that the axis
E
of this figure is fixed to a pole that is
placed vertically in the ground. The lower part of the spinning disk is enclosed in
(but does not touch) a heavy case. The case serves to orient the disk so that, under
the action of gravity, the spin axis,
CD
, will be horizontal. It is crucial to note,
however, that the disk is free to rotate about the axis
AB
if a torque is applied.
To see how a gyrocompass works, we can employ this conceptual model as
shown in figure A4.
3
Imagine our conceptual gyrocompass on a pole that is stuck
vertically in the ground, initially at position
a
. The heavy case, which is pulled by
gravity, ensures that the spin axis,
AB
of figure A3, is horizontal. A few hours later,
the earth has rotated the gyrocompass to position
b
. However, because of its
propensity to stay in the same orientation (due to the large angular momentum of
the fast-spinning disk), the spin axis is still horizontal. Gravity acts on the case to
pull it down, thus exerting a torque about the axis
AB
of figure A3. The direction of
the torque is out of the page, toward you.
4
Torque acts to change angular momen-
tum, so the direction of the spin (dashed arrows in fig. A4) is changed: the arrow
moves north, out of the page. Here is the gyrocompass beginning to do its thing—
aligning itself with the earth's spin axis by pointing north.
3. Real gyrocompasses do not resemble the model of figure A3, which is only for pedagogical
purposes. The explanation of gyrocompass behavior given here is close to that of a very early U.S.
Navy report on this device; see Gillmor (1912). For more information on modern gyro technol-
ogy, see Lawrence (1998). There is also a helpful online account of gyroscope use in maritime
navigation on a page of the San Francisco Maritime National Historic Park website, at
www.mari
4. This behavior is surprising: we expect the torque to pull the gyroscope as shown by the
curved arrow at
b
in fig. A4. Instead, it acts to pull the gyroscope out of the page. This odd
behavior is understood by physicists but is counterintuitive. The same behavior makes a child's
spinning top precess instead of fall over. The explanation lies in the manner in which angular
momentum vectors add: the
direction
of the torque is out of the page, according to the right-hand
rule discussed in the box ''Spinning Tops and Angular Momentum'' in chapter 8. This torque
vector is added to the gyroscope spin vector to produce the change of direction shown in fig. A4.
