We study a rotating atomic Fermi gas near a narrow
s-wave Feshbach resonance in a uniaxial trap with frequencies

![[perpendicular]](http://scitation.aip.org/stockgif3/perp-script.gif)
,
z. We predict the upper-critical angular velocity,
c2(

,
T), as a function of temperature
T and detuning

across the BEC-BCS crossover. The suppression of superfluidity at
c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low
T and
z

![[perpendicular]](http://scitation.aip.org/stockgif3/perp-script.gif)
, in the BCS and crossover regimes of 0



c,
c2 is implicitly given by
![[h-bar]](http://scitation.aip.org/stockgif3/planck.gif)
![sqrt( omega[sub c2][sup 2] + Omega[sub [perpendicular]][sup 2])](http://scitation.aip.org/servlet/GetImg?key=PRLTAO000097000025250401000001%3A0%3A0%3A28)
![[approximate]](http://scitation.aip.org/stockgif3/ap.gif)
2

![sqrt([h-bar] Omega[sub [perpendicular]]/epsilon[sub F])](http://scitation.aip.org/servlet/GetImg?key=PRLTAO000097000025250401000001%3A0%3A1%3A28)
, vanishing as
c2~

![[perpendicular]](http://scitation.aip.org/stockgif3/perp-script.gif)
(1-

/
c)
1/2 near
c![[approximate]](http://scitation.aip.org/stockgif3/ap.gif)
2
F+

Fln(
F/
![[h-bar]](http://scitation.aip.org/stockgif3/planck.gif)

![[perpendicular]](http://scitation.aip.org/stockgif3/perp-script.gif)
) (with

the BCS gap and

the resonance width), and extending the bulk result
![[h-bar]](http://scitation.aip.org/stockgif3/planck.gif)
c2
![[approximate]](http://scitation.aip.org/stockgif3/ap.gif)
2
2/
F to a trap. In the BEC regime of

<0 we find
c2


![[perpendicular]<sup>-</sup>](http://scitation.aip.org/servlet/GetImg?key=PRLTAO000097000025250401000001%3A0%3A3%3A28)
, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.