# radius of curvature

**Problem**

Determine the radius of curvature of the curve $x = y^3$ at point (1, 1).

A. 5.27 | C. 5.56 |

B. 5.65 | D. 5.72 |

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## Curvature and Radius of Curvature

**Curvature** (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average *change in direction* of the curve per *unit of arc*. Imagine a particle to move along the circle from point 1 to point 2, the higher the number of $\kappa$, the more quickly the particle changes in direction. This quick change in direction is apparent in smaller circles.

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## Simple Curves

**Formulas for Circular Curves**

The formulas we are about to present need not be memorized. All we need is geometry plus names of all elements in simple curve. Note that we are only dealing with circular arc, it is in our great advantage if we deal it at geometry level rather than memorize these formulas.

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