!!! Radius Of Curvature !!!

Classical Mechanics Level 3

A particle moves along the plane of trajectory y(x) with constant speed.Find the Radius Of Curvature of the trajectory at the point x=0, if the trajectory has the form of a parabola
Y = 0.25 ∗ x 2 0.25 * x^2 .


The answer is 2.

Rushi Rokad by Rushi Rokad , 24, India

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1 solution

Anish Puthuraya
Feb 13, 2014

The radius of curvature is mathematically defined as,

R = ∣ ( 1 + y ′ 2 ) 3 y ′ ′ ∣ \displaystyle R = |\frac{\left(\sqrt{1+y'^2}\right)^3}{y''}|

Setting y = 0.25 x 2 \displaystyle y = 0.25x^2 , and then x = 0 \displaystyle x=0 , we get,

R = 2 \displaystyle \boxed{R = 2}

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This is one of the methods to solve..

Rushi Rokad - 7 years, 3 months ago

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