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Experiments on the axial breathing mode in a rapidly rotating Bose-Einsteincondensate are examined. Assuming a cold cloud without thermal component, weshow that errors due to defocus of an imaging camera in addition to aninclination of the rotational axis can lead to a significant underestimate ofthe rotation rate in the fast rotation limit; within these uncertainties, ourtheoretical prediction agrees with the experimental data. We also show that, inthe fast rotation regime, the Thomas-Fermi theory, which is inapplicable there,underestimates the rotation rate. Underestimate of the rotation rate due tothese effects would also partly explain a discrepancy between theory andexperiment for the Tkachenko mode frequency in the fast rotation regime.Comment: 5 pages, 2 figures; this paper is related to cond-mat/0506331;  accepted for publication in Phys. Rev. A Rapid Communication

Axial breathing mode in rapidly rotating Bose-Einstein condensates and uncertainty of the rotation velocity