Grid warping, rotating frame

n = 8;
\[Omega] = 1/2;
p1s = Table[{-Sqrt[1 - y^2], y}, {y, -1, 1, 2/n}][[2 ;; -2]];
p1s2 = Table[{x, -Sqrt[1 - x^2]}, {x, -1, 1, 2/n}][[2 ;; -2]];
frame[\[Omega]_] :=
  Show[
   Graphics[Circle[], PlotRange -> 1.1],
   Table[
    ParametricPlot[
     RotationMatrix[\[Omega] (\[Tau] - 2 Pi)].(
       p1 Max[0, (1 - (\[Tau]/(2 Pi))/(-p1[[1]]))] + {-p1[[1]],
          p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[1]])]
       )
     , {\[Tau], -0.001, 2 Pi}, PlotStyle -> Thick, Axes -> None]
    , {p1, p1s}
    ],
   Table[
    ParametricPlot[
     RotationMatrix[\[Omega] (\[Tau] - 2 Pi)].(
       p1 Max[
          0, (1 - (\[Tau]/(2 Pi))/(-p1[[2]]))] + {p1[[
           1]], -p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[2]])]
       )
     , {\[Tau], -0.001, 2 Pi}, PlotStyle -> Thick]
    , {p1, p1s2}
    ]
   ];

Manipulate[frame[\[Omega]], {\[Omega], -0.5, 0.5}]