Rotations, Spin, and People

I hate to rotate. It makes me sick. And yet, every day I spin at 800 miles per hour, because living on a spinning earth does this to me. Why does the earth spin at all? [CalTech answer.] Did it always spin the way it does now? [No.] Could it spin in the other direction that would make the sun rise above the horizon in the West rather than the East? [No.] If not, why not? [Not sure yet.] I am pondering these questions as I will teach my first undergraduate class in ten days:

I plan to introduce how oceans and atmospheres circulate to distribute heat, water, and “stuff” like food and plastics across the globe. There is lots of rotation, lots of angular momentum, lots of torque and I am unsure, if a text book and lecture via Zoom will make much sense. So, today I discovered several fun and smart and insightful videos that I may even pose to my students as Homework or Exam questions 😉

The first set of videos I discovered today is Derek Muller’s Veritasium channel on YouTube. He covers a range of physics, math, and even biology topics, but I here focus on his wing nut problem. He entertains by explaining a strange and even bizarre observation made in space some 30 years ago. A Russian engineering astronaut noticed a rotating wing nut change its rotational axis repeatedly. Russia kept the observation top secret for over 10 years for reasons not entirely clear, but here is a modern attempt to explain what happened. It also applies to how tennis rackets rotate:

Now this reminded me of a problem that I encountered during my third year studying physics in Germany. I never solved or understood this so-called spinning-hard-boiled-egg problem that the Physics Girl describes so well. Her real name is Dianne Cowern and I use her videos in my graduate statistics class where her voice and physics shatters wine glasses via resonance. Today I discovered many more of her PBS Digital videos that all are filled with fun, beauty, and smart explanations. She plays with vortices in air and water and in between.

Now how does this relate to oceanography and meteorology? Well, we all live somewhere on the spinning top or egg or peanut that we call earth. Gravity keeps us grounded, but rotating objects can do strange things as the above two videos show. And when rotation becomes important we are not just dealing with linear momentum, but also angular momentum. When rotation becomes important, we must consider torques that generate angular momentum in ways similar to how forces generate linear momentum.

Rotation adds a strong and often counter-intuitive element because unlike a force that accelerates a car in the same direction that the force is applied, a force applied to a rotating system generates a torque perpendicular to both the force and the direction to the rotational axis. This can be confusing and one has to either watch the movies or go through advanced vector calculus. Furthermore, a rotating sphere acts differently than a rotating spheroid which acts differently from a rotating triaxial spheriod. Our peanut earth is the latter and thus has at least three axes of orientation (a and b and c) that all have different kinetic energy and angular momentum states. This makes for wobbly rotations which are sensitive to changes in both force balances and the distribution of masses like ice and water that can move to different locations at different times and stay there for a while.

For a perfect sphere three perpendicular lines from the center to the surface all have the same distance a (top) while for a spheriod only two of the three perpendicular lines have the same distance from the center (bottom right). If all three perpendiculars are different then we have something called a triaxial spheroid [Adapted from WikiPedia].

And how does this relate to climate science and my beloved glaciers in Greenland? Well, there is the “global wobbling” that caused ice ages and warm periods as the earth’s principal axis or rotation changes or wobbles. The “global wobble” was discussed in hilarious way a few years ago by the United States House of Representative’s “Committee on Science, Space, and Technology.” Closing this essay, I let Jon Steward of the Comedy Channel speak and hope you find his commentary and live experiment as funny as I do:

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