College
of William and Mary Petersburg, Virginia
I
The burning of cellulosic materials often produces smoke or vapor that has a swirling motion. Boiling water will often show spirals of steam, too. Tropical storms have a similar gyratory motion. The observance of swirling is so common with water and water-containing materials, that i t is presumed that the movements of the water molecules must be a t least partly responsible for gyrat.ion. The water molecule, as its structure is depicted in textbooks, looks similar to that of a boomerang. When thrown, a boomerang rotates on its center of mass and describes a circular path to return to the throm-er. It is conceivable that an upsurge of air beneath it could send it on a gyrating path. The mass distribution in a water molecule is different from that of a boomerang, so the idea of ~vaterbeing a molecular boomerang was discarded. However, the mass distribution equivalent to water could be mounted on a disk and spun like a gyroscope. The idea of water being a molecular gyroscope was therefore developed. A gyroscope is defined as a wheel or disk, called a rotor, having a uniformly-distributed mass, and rotating on its center of mass, usually at high velocity. For example, a simple gyroscopic top set to spinning by pulling a string wound around its axle, will attain a maximum velocity of about 2000 rpm. When a rotor is spinning in any position, i t will precess. If the rotor is supported through its center of mass by a horizontal axle, as shown in Figure 1, the axis of precession will be through the plane of the rotor and perpendicular to the rotational axis. When rotating, one face of the rotor will be turning clockwise and the other face counterclockwise. When the rotor is observed along the axis of precession, it will be seen to precess either clockwise or counterclockwise, too. If the observation is made downward, as in Figure 1, and the precession is clockwise, then the face of the rotor that is turning clockwise is taken as the reference face. The principles of high velocity gyroscopes have been well established, since these instruments are used on ships and rockets. The gyroscope is of interest in the study of molecular motion. Precession is more apparent as the rotational velocity decreases. This is shown by the slowing down of a spinning top. Because precession does seem to be a vector in the gyration of molecules, it can be assumed that rotational velocities might be relatively low. Observations were made by spinning
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' B I ~ N A LJ.,U.,
AND
Fow~~m R., H., J. o h m . Phy8. 1, 515
(1933).
MICKE, R.,AND BAWMANN, w.,Z . Physik
368
/
Journol of Chemicol Edumtion
33, 833 (1932).
the rotor by hand, and ranged from about 10-120 rpm. Every molecule has a center of mass. The mass is not necessarily concentrated a t the rim, or equally distributed, but i t can spin on its own center of mass. Any object rotating on its center of mass will precess. The combination of rotation and precession will be referred to as gyroscopic motion. Any body in gyroscopic motion resists the application of an outside force, as is evident when a top or bicycle wheel is held in the hand and an attempt is made to change its plane of rotation. If two molecules in gyroscopic motion approach one another, their charges must repel, changing the planes of rotation, and similarly exerting a resisting force. For example, if t\vo molecules were in parallel planes while rotating, as each precessed they would come into the same plane. Like charges would come closer together and repel. The molecules would resist the change, but would turn to reorient their planes. Water was described as having a tetrahedral structure by Bernal and Fowler.' The protons are 0.96 A from the oxygen at its center, and make an angle of 104.5" with it.z Figure 2 depicts the two axes of revolution. Let the rotor be represented by a thin section of the water molecule tetrahedron, including only the oxygen and protons. The electrons are excluded because their masses are nil (= proton mass X 1/1847). Their inclusion would contribute less than 0.2% to the equivalent of the proton. The rotor, then, represents the entire mass portion of the tetrahedron. A model of a water molecule was constructed from these data. First, a basic rotor was constructed. Using a 4 X 4 it sheet I/&. Masonite, a rotor of 29-in. radius was cut from it. It was pmtidly circular, as shown in Figure 3. The center of mass was determined by balancing it horieontally on the point of
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R"01"""" A",, of
Figure 1. Gyroscopic motion. A vertical dirk rotating on its center of mass, will have the axis and direction of precession or shown.
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I
H
Figwe 2. The depiction of the axes of revolution and precerrion of o molecule of water vapor.
Figure 3. A construction model of o molecule of water vapor. The model is not drawn to scale. Measurements were made to the nearest one-eighth of on inch, then rounded off.
of a nail, then a. in. hale was drilled. The rotor was suspended by a horizontal steel rod of '/
