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[answered] a\ Find the center of mass of the cylinder x^ 2+ y^ 21,1 z


? 6.3:

a Find the center of mass of the cylinder?x^2+y^2?1,1??z?? 2 if the density is ?=(x^2+y^2)z^2.


2 1 2 m dV E 2 2

 

2 r z rdzdrd 0 0 1 2 1 1 2 1 7 7

 

3

 

2

 

0 d 0 r dr 1 z dz 2 4 3 6 2 1 15 15

 

d r 3dr z 3dz 2 4 4

 

8

 

E

 

0

 

0

 

1

 

By symmetry of cylinder and density function,

 

M xy z dV M yz 0

 

M zx 0

 

Thus M...

 


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