1.5: Summary of the Formulas for Plane Laminas and Curves
- Page ID
- 6929
Uniform Plane Lamina |
\( y = y(x) \) | \( r = r(θ) \) |
\( \overline{x} = \frac{1}{A} \int_a^b xydx\) \( \overline{y} = \frac{1}{2A} \int_a^b y^{2}dx\) |
\( \overline{x} = \frac{2 \int_ \alpha ^ \beta r^3 cos \theta d \theta }{3 \int_ \alpha ^ \beta r^2 d \theta } \) \( \overline{y} = \frac{2 \int_ \alpha ^ \beta r^3 sin \theta d \theta }{3 \int_ \alpha ^ \beta r^2 d \theta} \) |
Uniform Plane Curve |
\( y = y(x) \) | \( r = r(θ) \) |
\( \overline{x} = \frac{1}{L} \int_a^b x[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}\) \( \overline{y} = \frac{1}{L} \int_a^b y[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}\) |
\( \overline{x} = \frac{1}{L} \int_ \alpha ^ \beta rcos \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2} \) \( \overline{y} = \frac{1}{L} \int_ \alpha ^ \beta rsin \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2} \) |