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현재 위치

Centroid, the y-direction centroid distance of the area surrounded by y = ax^n and the x-axis

작성자 Uploader : pleiades 작성일 Upload Date: 2019-03-07변경일 Update Date: 2019-10-22조회수 View : 369

As shown in the figure, the y-direction centroid distance Gy of the area surrounded by y = ax^n and the x-axis can be obtained as follows.

Gy = Mx / A

Mx : first moment of inertia relative to x axis
A : area

Mx = ∫y*(y/2) dx = ∫(1/2)*y^2 dx = ∫(1/2)*a^2*x^(2n) dx
= (a^2/2)(1/(2n+1))*x^(2n+1)

Since x = x1,

Mx = (a^2/2)(1/(2n+1))*x1^(2n+1)

A = ∫ y dx = ∫ a*x^n dx = (a/(n+1))*x^(n+1)

The area from 0 to x1 is :

A = (a/(n+1))*x1^(n+1)

Gy = (a^2/2)(1/(2n+1))*x1^(2n+1) / (a/(n+1))*x1^(n+1)
= (a*(n+1)/(4n+2))*x1^n

*** 참고문헌[References] ***

Gy = (a*(n+1)/(4*n+2))*x1^n


변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

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1st Step for All

현재 위치

Centroid, the y-direction centroid distance of the area surrounded by y = ax^n and the x-axis

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