Menurunkan rumus titik berat penampang setengah lingkaran
a. Terhadap sumbu X
\(X^{2}+Y^{2}=R^{2}\)
\(Y^{2}=R^{2}-X^{2}\)
\(Y \times A=\int \bar{y} \times dA\)
\(Y \times \left ( \frac{1}{2}\pi R^{2} \right )=\int \frac{y}{2} \times y \times dx\)
\(Y=\frac{\int \frac{y}{2}.y.dx}{\frac{1}{2}\pi R^{2}}\)
\(Y=\frac{\int y^{2}.dx}{\pi R^{2}}\)
\(Y=\frac{2\int_{0}^{R}\left ( R^{2}-X^{2} \right ).dx}{\pi R^{2}}\)
\(Y=\frac{2\left [ R^{2}X-\frac{X^{3}}{3} \right ]_{0}^{R}}{\pi R^{2}}\)
\(Y=\frac{2\left [ R^{3}-\frac{R^{3}}{3} \right ]}{\pi R^{2}}\)
\(Y=\frac{2\left [ \frac{2}{3}R^{3} \right ]}{\pi R^{2}}\)
\(Y=\frac{4R}{3\pi }\)
b. Terhadap sumbu Y
\(X= 0\)
Ditulis oleh : Civil Engineering Library