Practice Curvature Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A measure of how quickly a curve bends or deviates from being a straight line at a given point.
A tight turn has high curvature; a gentle bend has low curvature.
Example 1
easyA circle has radius r = 4 cm. What is its curvature \kappa? Compare with a circle of radius r = 1 cm.
Example 2
mediumTwo circular arcs lie along a road: arc A has radius 200 m (gentle bend) and arc B has radius 50 m (sharp bend). Calculate the curvature of each and explain which is safer to drive at high speed.
Example 3
easyA coin has diameter 2.4 cm. What is the curvature of its edge?
Example 4
hardThe osculating circle (circle of curvature) at a point on a curve has radius \rho. If the curvature at point P is \kappa = 0.4 cm^{-1}, find \rho. If the curvature doubles, what happens to \rho?