## An Equation For Radius of Curvature For a Curve in the xy Plane

For a curvein theplane, the radius of curvatureis given by

To show this writewhereandare unit vectors. with find

sinceandis perpendicular to

Hence

Then

For a curvein theplane, the radius of curvatureis given by

To show this writewhereandare unit vectors. with find

sinceandis perpendicular to

Hence

Then