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Engineering Calculus Notes 163

Engineering Calculus Notes 163 - 151 2.2 PARAMETRIZED...

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2.2. PARAMETRIZED CURVES 151 θ R θ Figure 2.20: Turning Wheel wheel is at (0 ,R ). We take as our parameter the (clockwise) angle θ which the radius to the point makes with the downward vertical, that is, the amount by which the wheel has turned from its initial position. When the wheel turns θ radians, its center travels units to the right, so the position of the center of the wheel corresponding to a given value of θ is −→ c ( θ ) = R −→ + ( ) −→ ı = ( Rθ,R ) . At that moment, the radial vector −→ r ( θ ) from the center of the wheel to the point on the rim is −→ r ( θ ) =
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