Center of Mass for Planar Region in Polar Coordinates - Maple Help

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Center of Mass for Planar Region in Polar Coordinates

Description

 

Determine r&conjugate0; and θ&conjugate0;, the center of mass  coordinates for a planar  region in polar coordinates .

 

Center of Mass for Planar Region in Polar Coordinates

Density:

r

r

(1)

Region: r1θr r2θ,aθb

r1θ

0

0

(2)

r2θ

1

1

(3)

a

0

0

(4)

b

π2

12π

(5)

Moments÷Mass:

Inert Integral - dr dθ

StudentMultivariateCalculusCenterOfMass, r=..,θ=..,coordinates=polarr, θ,output=integral

∫012π∫01cosθr3ⅆrⅆθ∫012π∫01r2ⅆrⅆθ,∫012π∫01sinθr3ⅆrⅆθ∫012π∫01r2ⅆrⅆθ

(6)

Explicit values for r&conjugate0; and θ&conjugate0;

StudentMultivariateCalculusCenterOfMass,r=..,θ=..,coordinates=polarr, θ

322π,14π

(7)

Plot:

StudentMultivariateCalculusCenterOfMass,r=..,θ=.., coordinates=polarr, θ,output=plot,caption=

Commands Used

Student[MultivariateCalculus][CenterOfMass]

Related Task Templates

Multivariate Calculus > Multiple Integration > Polar

See Also

Student[MultivariateCalculus, Student[MultivariateCalculus][MultiInt]


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