GraphingCalculator 4;
Window 46 6 840 1296;
PaneDivider 372;
FontSizes 18;
BackgroundType 0;
Slider 0 40;
SliderSteps 400;
SliderControlValue 0;
2D.BottomLeft -2.234375 -7.015625;
2D.Axes 0;
2D.GraphPaper 0;
Text "Rolling without slipping.

Speed of point on rim is V=WR.   With no slipping, in the rest frame of the wheel this must be the speed at which the ground moves past, which in turn must therefore be the speed of the wheel center as viewed from the rest frame of the ground.         

Radius and velocity of wheel:";
Color 2;
Expr R=1;
Color 4;
MathPaneSlider 122;
Expr V=slider([-2,2]);
Text "Toggle between rest frame of wheel (a=0) and rest frame of ground (a=1):";
Color 8;
MathPaneSlider 1;
Expr a=slider([0,1,1]);
Color 5;
Expr I=vector(1,0),J=vector(0,1),O=vector(0,0);
Text "Wheel/tank tread:";
Color 3;
Expr [x-(a*V*n)]^2+[y-R]^2=R^2,x<a*V*n;
Color 5;
Expr d=slider([0,5]);
Color 3;
Expr [x-(a*V*n)-d]^2+[y-R]^2=R^2,x>a*V*n+d;
Color 3;
Expr vector(a*V*n+t*d,0);
Color 3;
Expr vector(a*V*n+t*d,2*R);
Color 6;
Expr C=vector(V*a*n,R);
Color 17;
Expr C;
Color 7;
Expr C_1=vector(V*a*n+d,R);
Color 7;
Expr W=V/R;
Expr D=vector(-sin([W*n]),-cos([W*n])),T=vector(-cos([W*n]),sin([W*n]));
Text "Velocity in both frames:";
Color 17;
Expr C,C+I*a*V;
Color 17;
Expr J*h,J*h+I*[a-1]*V;
Color 3;
MathPaneSlider 73;
Expr h=slider([-0.1,0.1]);
Text "Point on rim and its velocity";
Expr C,C+D*R;
Expr C_1,C_1+D*R;
Color 17;
Expr C+D*R;
Color 17;
Expr C+D*R,C+D*R+T*V;
Text "Point of contact with ground";
Color 17;
Expr vector(a*V*n,-h);
Text "Ground:";
Color 17;
Expr y=0;
Color 4;
Expr y=0.02*cos([10*[x+[1-a]*V*n]]);
Text "

<size=15>Author: David A. Craig <<http://web.lemone.edu/~craigda/>";