15 May 2012

Ping-Pong Physics and Vlogging

One of my favorite results from Classical Mechanics has to do with the stability of rigid bodies as they rotate about certain axes.  I demonstrate this theorem in a YouTube video, which is my first attempt at vlogging (though these words may render my attempt but a partial one!).  Click on the video below (or click here) to see and hear me talking about rotating ping-pong paddles.  If you don't own a ping-pong paddle, try my demonstration at home with your television's remote control.  You should easily be able to find the axis about which rotation is unstable.  That's how I discovered one of nature's beautiful workings when I was a teenager.



3 comments:

  1. Sir, that's a good video. I knew the fact of sum of moment inertia about the two planar axis leads to MI about the perpendicular axis. I didn't know that the rotation about I2 is "unstable". Any reasons as to why is that?

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    1. The reason for rotational instability about the principal axis of inertia corresponding to the intermediate principal moment of inertia is tough to give, at least from a qualitative viewpoint. In a classical mechanics course, we learn that rigid-body motion depends on an object's structure via the principal moments of inertia. That means that if two objects share the same set of three numbers for the three principal moments of inertia, the rotational dynamics of each object is the same, even if the objects have different shapes. Cauchy noticed this in 1827 and Poinsot came up with his famous construction in 1834. Poinsot created what's known as an "equivalent ellipsoid" that one could study instead of the actual object of interest. As long as the equivalent ellipsoid has the same principal moments of inertia as the object of interest, one is okay studying the equivalent ellipsoid instead. If one creates such an ellipsoid, it's not difficult to see why instability arises for the intermediate moment of inertia. Unfortunately, it takes a little bit of mathematics to get to that "not difficult" point! See Chapter 11 of "Classical Dynamics of Particles and Systems" (5th ed) by Thornton and Marion or Chapter 5 of "Classical Mechanics" (3rd ed) by Goldstein, Poole, and Safko.

      Sorry that I don't have a better qualitative explanation! Besides a ping-pong paddle, you can try this out with a tennis racket or even a typical book (tape it shut first!). Any asymmetric wooden block will do nicely, too.

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