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In the 30 November 2000 issue of Nature, physicists Van den Engh and coworkers discuss experiments in which disks were spun in a vacuum.
They found that slippage between the disk and the surface could account for observations, and the presence or absence of air affected the disk's behaviour only slightly.
They pointed out that Moffatt's analysis would predict a very long wobbling time for a disk in a vacuum, which was not observed.

1.921 seconds.