Particle Moving on a Rotating Disk

Manipulate[With[{eqs={(t vx0+x0) Cos[(t/2)]+t (vy0+(x0/2)) Sin[(t/2)],t (vy0+(x0/2)) Cos[(t/2)]-(t vx0+x0) Sin[(t/2)]}},ParametricPlot[Evaluate[eqs],{t,0,(If[NumberQ[#1],#1,40]&)[Quiet@FindRoot[Evaluate[Plus@@(eqs^2)==1],{t,155,0,5000},MaxIterations->50][[1,2]]]},Prolog->{GrayLevel[.8],Disk[{0,0},1],PointSize[.02],GrayLevel[.0],Point[{0,0}]},PlotRange->{{-1,1},{-1,1}},Axes->False,PlotPoints->1000]],{{x0,.5,"initial position x"},0,1,Appearance->"Labeled"},{{vx0,-.0004,"initial velocity in x"},-0.1,.1,Appearance->"Labeled"},{{vy0,.23,"initial velocity in y"},-.24,.24,Appearance->"Labeled"}]

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Particle Moving on a Rotating Disk" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ParticleMovingOnARotatingDisk/

Contributed by: Enrique Zeleny

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