Cos Roll

Manipulate[
 Module[{\[Theta]},
  \[Theta] = Pi Sin[2 Pi t];
  Show[
   Graphics[{
     {RGBColor[0.85, 0.88, 0.9], EdgeForm[RGBColor[0.65, 0.68, 0.7]],
      Disk[{\[Theta], 0}, 1]},
     {RGBColor[0.65, 0.68, 0.7],
      Disk[{\[Theta], 0} + 0.5 {Sin[-\[Theta]], Cos[-\[Theta]]}, 0.5]},
     {RGBColor[0.5, 0.1, 0.1],
      Line[Accumulate[{{\[Theta], 0},
         0.5 {Sin[-\[Theta]], Cos[-\[Theta]]},
         0.5 {Sin[\[Theta]], Cos[\[Theta]]}}]]}
     }, PlotRange -> {{-Pi - 1.1, Pi + 1.1}, {-1.1, 1.1}},
    ImagePadding -> 10],
   Plot[Cos[tt], {tt, -Pi - 0.01, \[Theta]},
    PlotStyle -> RGBColor[0.2, 0.1, 0.1]]
   ]
  ]
 ,
 {t, 0, 1}]