An Equation For Radius of Curvature For a Curve in the xy Plane
For a curve
in the
plane, the radius of curvature
is given by
To show this write
where
and
are unit vectors. with find
since
and
is 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