  An exactly solvable model of two-component interacting Fermi vapour in two
dimension within Thomas Fermi approach has been proposed. We assume a realistic
off-diagonal s-wave interaction between fermions in the two hyperfine states.
The interaction is taken to be given by a screened Coulomb interaction which is
both relevant and is analytically tractable. There are two distinct limits in
the case of trapped fermionic systems: When the rotating frequency is less than
the trap frequency a Thomas-Fermi approach may be used for a reasonably large
number of particles. In the case of rapidly rotating fermions, an alternative
variational approach is used, where the local density approximation may be
applied after projecting the system on to the lowest degenerate level. Analytic
expressions for the relevant physical quantities are obtained and their
significance is discussed in both these cases.
