Spin – hard to avoid, hard to understand

 kw: book reviews, nonfiction, science, spin, rotation, angular momentum

Imagine a universe that consists of two identical objects. They can be single atoms such as helium (hydrogen prefers to exist as H₂ molecules, which complicates matters). Imagine further that these two atoms are some distance apart, initially with zero velocity with respect to each other. The only force acting on them is mutual gravitational attraction. Finally, consider that the same quantum mechanical laws apply to this universe as to our own.

Right away there is a puzzle. Quantum uncertainty, or Heisenberg's Uncertainty Principle, requires that the position and velocity of these atoms cannot be known with certainty. Therefore, as they begin to approach one another under the influence of gravity, it is not certain that they will collide. Some component of their velocities is bound to be off-center, and it is almost certain that they will miss. At the instant of closest approach, from the point of view of an imaginary observer exactly between them, they are moving at almost (but not exactly) equal speed, in opposite directions, at right angles to the direction of the line between them. Thus, they are in orbit about their common gravitational center. This universe now contains spin: a pair of neural helium atoms rotating about a common center.

To be sure, their orbits will be rather elongated, and at their greatest extent, they will be nearly stationary. But following their orbits, and doing the calculations, you would find that their combined angular momentum is constant throughout their orbits.

What is angular momentum? For two identical objects rotating about a common center, angular momentum is the product of the total mass times the velocity of each object relative to the common center, divided by the distance of each object from the center of rotation (the radius). For spinning solid objects such as tops or planets or Frisbees the definition (and calculations) are more complex, but similar in principle.

Now we can look at our universe as it is. The current cosmological theory states that after the initial expansion from a primordial singularity (the Big Bang), followed by "inflation", once the universe had expanded enough for its general temperature to allow atoms and molecules to form, all the universe was permeated by nearly uniform gas, about 75% hydrogen and 25% helium by weight. Quantum fluctuations led to broad volumes having a range of densities. I have usually read that the variation in density was around one part in 10,000. That was enough to cause the denser areas to begin to condense under mutual gravitational attraction. After billions of years the result is a sky full of stars, clusters, galaxies, galaxy clusters, superclusters, and most likely even larger structures that span large proportions of the entire universe.

AND EVERYTHING IS SPINNING (but not real Tasmanian devils)

In the book The Science of Spin: How Rotational Forces Affect Everything From Your Body to Jet Engines and the Weather, author Roland Ennos begins, not with the scenario presented above, but with an early airplane that was prone to crashing because of the angular momentum of its engine. The original Sopwith Camel was too powerful for its own good. How the WWI pilots and flight engineers solved this problem introduces the book's subject.

The book has twenty chapters, and thus twenty subjects. More than I thought there would be. The first five chapters (Part I) deal in detail with Earth. Rotation of the gas-and-dust cloud that condensed into the solar system allowed planets to form around the nascent star. The tides that follow the rotation of Earth under sun and moon, coupled with the temperature-evening-out effect of Earth spinning, made the planet habitable.

There is a thorough discussion of Coriolis phenomena, often called Coriolis forces, which result from initially linear motions across the surface of a spinning planet. In the absence of planetary rotation, air heated at the equator would rise, then move poleward, replaced by colder air from the pole that descends and moves equatorward along the surface. There would be a perpetual north wind in the northern hemisphere and a perpetual south wind in the southern hemisphere. Earth's rotation causes the upper-level air that begins to move northward to be deflected to the left, leading to east-to-west winds by about 30° N latitude, which then descends and is deflected as it is returning to the equator. This is the Hadley Cell. Two more bands form, one in temperate latitudes and another in the Arctic. A similar pattern is mirrored in the southern hemisphere. I note that the striped pattern on Jupiter reveals that this huge planet, more than ten times the diameter of Earth, but spinning more than twice as fast (in RPM terms), must experience much greater Coriolis effects, since there are apparently 30-32 zones of alternating higher-speed and lower-speed wind.

Eight chapters make up Part II, regarding the development of technology, and in particular the role played by rotating machinery. The history is fascinating, but rather overwhelming; there is so much of it. There is a little about conversions between rotatory motions and reciprocating motions; think of the rotating crankshaft in an internal combustion engine, coupled to the piston, which moves up-and-down or back-and-forth. Such conversions and similar themes are more the subject of Part III and its five chapters about the human body. To me, the culmination of the section is the discussion of throwing. 

The human shoulder joint is made for strong, accurate throwing, in contrast to the shoulder joints of all the other apes. This is why no chimpanzee or gorilla could become a baseball pitcher. Shoulder, elbow, wrist; each contributes to increasing the velocity of a throw, and each equally allows increased control for accurate throwing. By itself, the forearm is a sling pivoted on the elbow from the upper arm. The hand, pivoting on the wrist, is a secondary sling with an extra function: It allows a thrower or pitcher to spin the projectile, which stabilizes it in flight.

There is a great discussion of the mechanics of the trebuchet, or counterweigh catapult. This image is from the Ancient Technology website.

The throwing arm is driven by the heavy counterweight. The rope sling, with one end firmly attached and the other on a slip peg for release at the correct angle, adds great acceleration to the projectile. Take note of the angle of the counterweight in each diagram. The length of its attachment to the throwing arm determines when it "cocks", suddenly slowing the arm and facilitating release of the rope sling at the proper angle. This also facilitates accuracy.

I have made several small trebuchets for demonstration purposes. I helped our son and a friend of his build one for Science Olympiad on two occasions. The Olympiad had a "Storm the Castle" event for a few years. A catapult had to fit in a one meter cube when ready to throw. This is a view of several competing catapults awaiting the competition. Ours is at front and center.

The last two chapters, that make up Part IV, are a review of some historical point, and a backhanded complaint about the use of "spin" as a political term for biased reporting. Physically spinning may make you dizzy and confused. Being politically "spun" has a similar effect on one's understanding of current events.

It becomes clear that, while the mechanics of a single rotating object such as a planet or a top can be described with great exactness in an equation or two, the mechanics of a sports throw or the action of a trebuchet have no "closed form" mathematical treatment. Growing up in a physical body, we learn how certain aspects of spin work, in an intuitive and bodily way. We understand things "in our gut" far beyond what the math can discern. I am concerned for a generation of "digital natives" that have never gone outside to throw a ball around, or swing on a swing.

Amidst reading, I was sometimes irked at the length of explanations. But each time I had finished a portion, I realized I had learned something that a shorter treatment might have left unrealized. I am glad I read this book.

Errata: 

• On page 8: "Neptune … spins on its side." It is Uranus that is tilted almost parallel to it orbital plane.
• On page 38: Discussing the effect of Earth's spin on solar heating, "…alternately heated by the action of the sun during the day and allowed to cool when on the far side of the sun…" The last few words need to be either "on the far side of the Earth" or "on the far side away from the sun". The "far side" of the sun itself is just as hot as the near side!