Curvature Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A coin has diameter 2.42.4 cm. What is the curvature of its edge?

Solution

  1. 1
    Step 1: Radius =2.42=1.2= \dfrac{2.4}{2} = 1.2 cm.
  2. 2
    Step 2: Curvature ฮบ=1r=11.2=56โ‰ˆ0.833\kappa = \dfrac{1}{r} = \dfrac{1}{1.2} = \dfrac{5}{6} \approx 0.833 cmโˆ’1^{-1}.

Answer

ฮบโ‰ˆ0.833\kappa \approx 0.833 cmโˆ’1^{-1}
The curvature of a circle equals the reciprocal of its radius. Always convert diameter to radius first. Smaller objects have higher curvature โ€” a coin curves much more sharply than a bicycle wheel.

About Curvature Intuition

A measure of how quickly a curve bends or deviates from being a straight line at a given point.

Learn more about Curvature Intuition โ†’

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Example 4 hard

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