Moments of Inertia In Exercises 57 and 58, verify the moments of inertia for the solid of uniform density. Use a computer algebra system to evaluate the triple integrals. I x = 1 12 m ( 3 a 2 + L 2 ) I y = 1 2 m a 2 I z = 1 12 m ( 3 a 2 + L 2 )
Moments of Inertia In Exercises 57 and 58, verify the moments of inertia for the solid of uniform density. Use a computer algebra system to evaluate the triple integrals. I x = 1 12 m ( 3 a 2 + L 2 ) I y = 1 2 m a 2 I z = 1 12 m ( 3 a 2 + L 2 )
Solution Summary: The author explains the formulae used to determine the mass of the solid.
Moments of Inertia In Exercises 57 and 58, verify the moments of inertia for the solid of uniform density. Use a computer algebra system to evaluate the triple integrals.
I
x
=
1
12
m
(
3
a
2
+
L
2
)
I
y
=
1
2
m
a
2
I
z
=
1
12
m
(
3
a
2
+
L
2
)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Calculate the fluid force on one side of the plate
The fluid force on one side of the plate is
using the coordinate system shown below. Assume
Ib.
the density is 62.4 lb/ ft3.
...
у (f)
Surface of pool
x (ft)
-у3 — 2
Depth
\y|
(x,y)
7
Please provide Handwritten answer.
Advanced Math
We consider a thin plate occupying the region D located in the upper half-plane (where y ≥ 0) and between the parabolas of equations : y = 2 - x2 and y = 1 - 2x2
The density of the plate is proportional to the distance from the x axis.
a) Calculate the moments of inertia (second moments) of the plate with respect to the coordinate axes.b) Is it easier to rotate the plate around the x-axis or the y-axis? Justify your answer.
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Find the circulation of F = -yi + x²j + zk around the oriented boundary of the part
of the paraboloid z = 9 - x² - y² lying above the xy-plane and having the normal
vector pointing upward.
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