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Viscous dissipation for Euler's disk
1Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, California 93106, USA. bildsten@kitp.ucsb.edu
Summary
This study corrects Moffatt's spinning coin calculation by including viscous boundary layer effects, improving the model for air dissipation. Rolling friction may be a more significant factor in the coin's decay than previously thought.
Area of Science:
- Fluid dynamics
- Physics of rotating objects
Background:
- Moffatt's prior calculation on viscous dissipation under a spinning coin.
- The importance of the viscous boundary layer's finite width was overlooked.
Purpose of the Study:
- To refine the calculation of viscous dissipation for a spinning coin.
- To develop a more accurate scaling law for the decay of a spinning coin's angle.
Main Methods:
- Incorporating enhanced dissipation within the viscous boundary layer.
- Comparing theoretical scaling laws with observed data.
Main Results:
- The revised model, including finite boundary layer width, shows better agreement with observed coin angle decay.
- Enhanced dissipation in the boundary layer leads to greater energy loss from circulating air.
Conclusions:
- Moffatt's calculation requires revision to account for boundary layer effects.
- Rolling friction represents a potentially dominant damping mechanism for spinning coins, surpassing air dissipation.