Rotational Stability

Time for an experiment! Find a book and secure it shut using tape or a rubber band. Now experiment with spinning the book while tossing it into the air. You’ll notice that when the book is spun about its longest or shortest axis it rotates stably, but when spun about its intermediate-length axis it quickly wobbles out of control.

Every rigid body has three special, or principal axes about which it can rotate. For a rectangular prism — like the book in our experiment — the principal axes run parallel to the shortest, intermediate-length, and longest edges, each going through the prism’s center of mass. These axes have the highest, intermediate, and lowest moments of inertia, respectively.

When the book is tossed into the air and spun, either about its shortest or longest principal axis, it continues to rotate about that axis forever (or until it hits the floor). For these axes, this indefinite, stable rotation occurs even when the axis of rotation is slightly perturbed.

When spun about its intermediate principal axis, though, the book also continues to rotate about that axis indefinitely, but only if the axis of rotation is exactly in the same direction as the intermediate principal axis. In this case, even the slightest perturbation causes the book to wobble out of control.

The first simulation above shows a rotation about the unstable intermediate axis, where a slight perturbation causes the book to wobble out of control. The second and third simulations show rotations about the two stable axes.

Unfortunately, as far as my understanding goes, there’s no intuitive, non-mathematical explanation as to why rotations about the intermediate principal axis are unstable. If you’re interested, you can find the stability analysis here.

`Mathematica code posted here.`

A few days ago, we found out that comet 67P/Churyumov–Gerasimenko is a contact binary. Now we have rotating view of it. This gif uses 36 images each separated by 20 minutes to show a 360° view of the comet. It takes the comet 12.4 hours to complete one rotation.

(via astronomynerd)

# Neil Whosis? What You Don’t Know About The 1969 Moon Landing

Forty-five years ago, this week, 123 million of us watched Neil and Buzz step onto the moon. In 1969, we numbered about 200 million, so more than half of America was in the audience that day. Neil Armstrong instantly became a household name, an icon, a hero. And then — and this, I bet, you didn’t know — just as quickly, he faded away.

"Whatever Happened to Neil Whosis?" asked the Chicago Tribunein 1974.

This is a missing chapter in the space exploration story. We like to think that after Apollo 11, the first duo on the moon became legendary. We know the names Aldrin and Armstrong now (or, at least many of us do), and we imagine they’ve been honored and admired all this time, the way we honor our favorite presidents, athletes, and war heroes. But that’s not what happened.”

Read more from Robert Krulwich at NPR.

A Mosaic of the Tarantula Nebula

"The Tarantula Nebula (also known as 30 Doradus, or NGC 2070) is an H II region in the Large Magellanic Cloud (LMC). It was originally thought to be a star, but in 1751 Nicolas Louis de Lacaille recognized its nebular nature.

The Tarantula Nebula has an apparent magnitude of 8. Considering its distance of about 49 kpc (160,000 light-years), this is an extremely luminous non-stellar object. Its luminosity is so great that if it were as close to Earth as the Orion Nebula, the Tarantula Nebula would cast shadows. In fact, it is the most active starburst region known in the Local Group of galaxies. It is also one of the largest such region in the Local Group with an estimated diameter of 200 pc. The nebula resides on the leading edge of the LMC, where ram pressure stripping, and the compression of the interstellar medium likely resulting from this, is at a maximum. At its core lies the compact star cluster R136 (approximate diameter 35 light years) that produces most of the energy that makes the nebula visible. The estimated mass of the cluster is 450,000 solar masses, suggesting it will likely become a globular cluster in the future.”

Richard Feynman discusses why there is a difference between the past and the future, in this clip from his legendary 1964 lecture series at Cornell: The Character of Physical Law.

It’s well worth taking 45 minutes out of your day to hear Dr. F explain why the workings of nature unfold in one direction. You see, while we innately know that the future is different from the past, and so much of our conscious experience is built around the fundamental just-so-ness of time moving forward, the equations of physics describing phenomena from gravity to friction can be run in either direction without breaking the rules. Yet irreversibility is what we observe.

That’s where entropy and probability come into play. When we take into account complex systems, like the jiggles and wiggles of the uncountable atoms that make up our bodies and this chair and my coffee and our world and even out to the scale of the universe itself, there is simply a greater chance that things will become more disordered than less. It’s not that the universe can’t run in reverse, it’s just that there are so many other ways for it not to.

Or as Feynman says, nature is irreversible because of “the general accidents of life”.

This seven-part series, which Open Culture has assembled in its entirety, captures the physicist in his prime, one year before he won the Nobel Prize and became a household name. Feynman was seemingly born for the scientific stage. He had this uncanny ability to weave profound observations of the universe’s inner workings with off-the-cuff (and often brash) humor. James Gleick wrote of Feynman’s unique style and skill:

He had a mystique that came in part from sheer pragmatic brilliance–in any group of scientists he could create a dramatic impression by slashing his way through a difficult problem–and in part, too, from his personal style–rough-hewn, American, seemingly uncultivated.

This clip was a huge influence on my recent video Why Does Time Exist? Although my take scarcely measures up to Dr. Feynman, you can watch below:

te coule un drôle de regard: Surface of Mars, photographed by Mars Express, 23rd December 2008.

1°N to 14°S, 64°E on the Terra Tyrrhena. For scale, Verlaine Crater - divided between the 5th and 6th images - is about 40 km across. The crater at bottom left of the 7th image is only a few degrees north of this gif.

Verlaine Crater is named after Verlaine, a village of about 3,500, rather than the groundbreaking queer poet Paul-Marie Verlaine (1844-1896). Curiously the IAU record the village as being in France, while it appears to be in the largely French-speaking Walloon Region of Belgium.

Composite of 3 visible light images for colour, and 1 monochrome image for detail.

Image credit: ESA. Composite: AgeOfDestruction.