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The mass moment of inertia of the wire with respect to
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Answer to Problem B.37P
The mass moment of inertia of the wire with respect to
The mass moment of inertia of the wire with respect to
The mass moment of inertia of the wire with respect to
Explanation of Solution
Given information:
The diameter of the formed steel wire is
The below figure represent the schematic diagram of the wire.
Figure-(1)
Expression of mass of the steel wire.
Here, density of the steel wire is
Expression of density of the steel wire.
Here, the specific weight of the steel wire is
Substitute
For section (1).
Substitute
Expression of volume of the steel wire after formation for section (1).
Here, the diameter of the formed wire is
For section (2).
Substitute
Expression of volume of the steel wire after formation for section (2).
For section (3).
Substitute
Expression of volume of the steel wire after formation for section (3).
For section (4).
Substitute
Expression of volume of the steel wire after formation for section (4).
Expression of Moment of inertia about
Here, the moment of inertia of section (1) about the
Expression of moment of inertia of section (1) about the
Expression of moment of inertia of section (2) about the
Expression of moment of inertia of section (3) about the
Expression of moment of inertia of section (4) about the
Expression of Moment of inertia about
Here, the moment of inertia of section (1) about the
Expression of moment of inertia of section (1) about the
Expression of moment of inertia of section (2) about the
Expression of moment of inertia of section (3) about the
Expression of moment of inertia of section (4) about the
Expression of Moment of inertia about
Here, the moment of inertia of section (1) about the
Expression of moment of inertia of section (1) about the
Expression of moment of inertia of section (2) about the
Expression of moment of inertia of section (3) about the
Expression of moment of inertia of section (4) about the
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the mass moment of inertia of the wire with respect to
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the mass moment of inertia of the wire with respect to
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the mass moment of inertia of the wire with respect to
Conclusion:
The mass moment of inertia of the wire with respect to
The mass moment of inertia of the wire with respect to
The mass moment of inertia of the wire with respect to
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Chapter B Solutions
Vector Mechanics For Engineers
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