2.2. PARAMETRIZED CURVES151θ RθFigure 2.20: Turning Wheelwheel is at (0,R). We take as our parameter the (clockwise) angleθwhichthe radius to the point makes with the downward vertical, that is, theamount by which the wheel has turned from its initial position. When thewheel turnsθradians, its center travelsRθunits to the right, so theposition of thecenterof the wheel corresponding to a given value ofθis−→c(θ) =R−→+ (Rθ)−→ı= (Rθ,R).At that moment, the radial vector−→r(θ) from the center of the wheel tothe point on the rim is−→r(θ) =
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