center of mass

**harry** · June 5th 2007, 12:07 PM

Find Mx , My and (xbar,y bar) for the laminas of uniform density p bounded by the graphs of the equations.
5. y= sqrt(x), y=x
6. x= -y, x=2y, x= 0

**ThePerfectHacker** · June 5th 2007, 12:50 PM

Originally Posted by harry

5. y= sqrt(x), y=x

$M = \iint_D dA = \int_0^1 \int_x^{\sqrt{x}} dy \ dx = .1666$

$M_x = \iint_D y \ dA = \int_0^1 \int_x^{\sqrt{x}} y \ dy\ dx = .0833$

$M_y = \iint_D x \ dA = \int_0^1 \int_x^{\sqrt{x}} x\ dy \ dx = .0667$

$\bar x = \frac{M_y}{M} = \frac{.0667}{.1666} = .4$

$\bar y = \frac{M_x}{M} = \frac{.0833}{.1666} = .5$

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