centroides

CENTROIDES DE SUPERFICIES Rectángulo

y

A = bh

b

xC = b / 2 yC = h / 2

•

yC

h x

xC

Triángulo rectángulo A = bh / 2

y h •

yC

xC = 2b / 3 yC = h / 3

Triángulo escaleno

x

xC b y

A = bh / 2 xC = (a + b) / 3 yC = h / 3

h •

yC xC

x b a

Cuadrante circular A = πR2 / 4

y •

yC

xC = 4R / 3π yC = 4R / 3π

Sector circular A = αR2 xC = (2R senα) / 3α yC = 0 (ángulo α en radianes)

R

xC

x

y R

α α

xC

•

x

CENTROIDES DE SUPERFICIES y

Semicírculo A = πR2 / 2

•

yC

xC = R yC = 4R / 3π

Cuadrante de elipse (

R

xC

x2 y2 + = 1) a2 b2

A = πab / 4 xC = 4a / 3π yC = 4b / 3π

x

y b •

yC yC

a

xC

x

y

Superficie de parábola ( y ∼ x2 ) A = 2bh / 3

h

xC = 5b / 8 yC = 2h / 5

•

yC 0

b

xC

y

Superficie de parábola ( y ∼ x2 ) A = bh / 3 xC = 3b / 4 yC = 3h / 10

h •

yC 0

Superficie de parábola ( y2 ∼ x )

b

xC

x

y

A = 2bh / 3 xC = 3b / 5 yC = 3h / 8

x

h

•

yC xC

b

x

CENTROIDES DE LINEAS Arco de circunferencia

y

L = 2αR R xC = (R senα) / α yC = 0 (ángulo α en radianes

α α

•

x

xC

Cuadrante de circunferencia

y

L = πR / 2

•

yC

xC = 2R / π yC = 2R / π

R

xC

x

y Semicircunferencia L = πR xC = R yC = 2R / π

•

yC xC

R

x