Radius of curvature
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Radius of Curvature - Questions: Exercise 1A - Problems on finding the radius of
(1) Find the curvature of the curves [Equation goes here - download the original to see it.] at the coordinate origin. (2) Find the curvature of [Equation goes here - download the original to see it.] at the vertices [Equation goes here - download the original to see it.] and [Equation goes here - download the original to see it.] . (3) Prove that the curvature of [Equation goes here - download the original to see it.] varies from -1 to 1 during one cycle. (4) Give the formula of the curvature of a polar equation [Equation goes here - download the original to see it.] (5) Find the curvature of the logarithmic spiral. (6) Find the curvature of the cycloid (i) using the intrinsic equation [Equation goes here - download the original to see it.] (ii) using the parametric equations [Equation goes here - download the original to see it.] (7) Find the curvature of epicycloids, given by the equation [Equation goes here - download the original to see it.] (8) Calculate the curvature of the [Equation goes here - download the original to see it.] Solution Exercise 1A (1) [Equation goes here - download the original to see it.] . At the origin, [Equation goes here - download the original to see it.] Therefore, the curvature is [Equation goes here - download the original to see it.] (2) We use the parametric equation of the ellipse, i.e. [Equation goes here - download the original to see it.] Therefore, the curvature is [Equation goes here - download the original to see it.] , where [Equation goes here - download the original to see it.] So [Equation goes here - download the original to see it.] At [Equation goes here - download the original to see it.], i.e. for [Equation goes here - download the original to see it. , we have [Equation goes here - download the original to see it.] At [Equation goes here - download the original to see it.], i.e. for [Equation goes here - download the original to see it.] , we have [Equation goes here - download the original to see it.]
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Contents of
Radius of curvature
1 Radius of Curvature - Questions: Exercise 1A - Problems on finding the radius of
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