Center of Mass for 3-D Region in Cylindrical Coordinates - Maple Help

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Center of Mass for 3-D Region in Cylindrical Coordinates

Description

 

Determine r&conjugate0;, θ&conjugate0;, and z&conjugate0;, the center of mass  coordinates for a 3-D region in cylindrical coordinates .

 

Center of Mass for 3-D Region in Cylindrical Coordinates

Density:

z

z

(1)

Region: z1r,θzz2r,θ,r1θrr2θ,aθb

z1r,θ

r

r

(2)

z2r,θ

1

1

(3)

r1θ

0

0

(4)

r2θ

1

1

(5)

a

0

0

(6)

b

π3

13π

(7)

Moments ÷ Mass:

Inert Integral - dz dr dθ

 

StudentMultivariateCalculusCenterOfMass,z=..,r=..,θ=..,coordinates=cylindricalr,θ,z,output=integral

∫013π∫01∫r1cosθr2zⅆzⅆrⅆθ∫013π∫01∫r1rzⅆzⅆrⅆθ,∫013π∫01∫r1sinθr2zⅆzⅆrⅆθ∫013π∫01∫r1rzⅆzⅆrⅆθ,∫013π∫01∫r1z2rⅆzⅆrⅆθ∫013π∫01∫r1rzⅆzⅆrⅆθ

(8)

Explicit values for r&conjugate0;, θ&conjugate0;, and z&conjugate0;, the center of mass given in cylindrical coordinates:

StudentMultivariateCalculusCenterOfMass,z=..,r=..,θ=..,coordinates=cylindricalr,θ,z

85π,16π,45

(9)

Commands Used

Student[MultivariateCalculus][CenterOfMass]

Related Task Templates

Multivariate Calculus > Multiple Integration > Cylindrical

See Also

Student[MultivariateCalculus, Student[MultivariateCalculus][MultiInt]


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