Enter your keyword

RADIUS OF CURVATURE FORMULA

The radius of approximate circle at a particular point is radius of curvature. The curvature vector length is the radius of curvature. The radius changes as the curve moves. Denoted by R, the radius of curvature is found out by the following formula:

\[\large R=\frac{(1+(\frac{dy}{dx})^{2})^{3}}{|\frac{d^{2}y}{dx}|}\]

Solved Examples

Question: Find the radius of curvature for the cubic at the point x = 2 ?

Solution: 

$Y = 5x^{3}-x+1$
x=2

$\frac{dy}{dx}=10^{2}+1$

$\left(\frac{dy}{dx}\right)^{2}=\left(10^{2}-1\right)^{2}$

$=100x^{4}-20x^{2}+1$

$=\frac{d^{2}y}{dx}=20x^{2}$

Using the formula

$R=\frac{(1+(\frac{dy}{dx})^{2})^{3}}{|\frac{d^{2}y}{dx}|}$

$R=\frac{\left(1+100x^{4}-20x^{2}+1\right)^{\frac{3}{2}}}{\left|20x\right|}\; at\;x=2$

$R=1481.51$

 

Related Formulas
Area of a Sector of a Circle FormulaArc Length Formula
Cube Root FormulaArea of a Rhombus Formula
Cofactor FormulaComplex Number Division Formula
Combination FormulaChi Square Formula