The authors consider a system of \(N\) particles moving with constant speed \( c\in \mathbb{R}^{2}\). Let \((X_{k}(t),V_{k}(t))_{k=1,\cdots ,N}\) be the positions and normalized velocities of the particles. The authors assume that the particle \(k\) is submitted to its proper angular velocity \(W_{k}\), to independent Brownian white noises \(P_{V_{k}^{\perp }}\circ (\sqrt{2D} dB_{t}^{k})\) and finally that it relaxes towards the neighbors’ average velocity \(\overline{V}_{k}\). The authors thus obtain the stochastic coupled system of equations \[ \begin{aligned} &\frac{dX_{k}}{dt}=cV_{k}, \\ &dV_{k}=P_{V_{k}^{\perp }}\circ (\nu \overline{V}_{k}dt+\sqrt{2D}dB_{t})+W_{k}V_{k}^{\perp }dt.\end{aligned} \] Considering the case where the number \(N\) of particles increases to infinity, they end with the Fokker-Planck equation \[ \partial _{t}f^{\varepsilon }+\nabla _{x}\cdot (vf^{\varepsilon })+\frac{1}{\eta } W\nabla _{v}\cdot (v^{\perp }f^{\varepsilon })=\frac{1}{\varepsilon } Q(f^{\varepsilon })=\frac{1}{\varepsilon }(-\nabla _{v}\cdot (P_{v^{\perp }} \overline{v}_{f^{\varepsilon }}^{\varepsilon }f^{\varepsilon }=+d\Delta _{v}f^{\varepsilon }). \] Considering first \(\eta =1\), the authors give the structure of the limit \(f^{0}\) of \(f^{\varepsilon }\) assuming that this limit \(f^{0}\) exists and that the convergence is as regular as needed. A quite similar result if then proved assuming now that \(\eta =\varepsilon \). The authors study the limit problem which is obtained in this case, leading to a new hydrodynamical model. In the last part of their paper, the authors consider the case where \(\eta =\varepsilon \zeta \) and they describe the limit problem which is here obtained and study its dependence with respect to \(\zeta \). The paper is completed with four appendices giving either the proofs of intermediate results or graphical representations.