Skip to main content
\(\require{cancel}\)
Physics LibreTexts

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

    \( y = y(x) \) \( r = r(θ) \)

    \( \overline{x} = \frac{1}{L} \int_a^b x[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}\)

    \( \overline{y} = \frac{1}{L} \int_a^b y[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}\)

    \( \overline{x} = \frac{1}{L} \int_ \alpha ^ \beta rcos \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2} \)

    \( \overline{y} = \frac{1}{L} \int_ \alpha ^ \beta rsin \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2} \)