Concept explainers
The mass moment of inertia of the wire with respect to
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
Want to see more full solutions like this?
Chapter B Solutions
Vector Mechanics For Engineers
- A section of sheet steel 0.03 in. thick is cut and bent into the sheet metal machine component shown. Determine the mass moment of inertia of the component with respect to each of the coordinate axes. (The specific weight of steel is 490 lb/ft3.)arrow_forwardThe uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values m = 9.7 kg and b = 650 mm. Answers: Ixx = i lyy= Izz i i kg-m² kg.m² kg.m²arrow_forwardQ3: Determine the moment of inertia about the CD axis. Fig (3)arrow_forward
- It is known that for a given area Iy = 48 x 106 mm4 and Ixy = -20 x 106 mm4, where the x and y axes are rectangular centroidal axes. If the axis corresponding to the maximum product of inertia is obtained by rotating the x axis 67.5° counterclockwise about C , use Mohr’s circle to determine (a) the moment of inertia Ix of the area, (b) the principal centroidal moments of inertia.arrow_forwardBy the method of this article, determine the moments of inertia about the x-and y-axes of the trapezoidal area. 1.5b 1.5b 1.3b b Answers: Ix= i ba baarrow_forwardThe machine element shown is fabricated from steel, where h = 64 mm. The density of Steel is y 40 mm 20 mm- 80 mm 40 mm 20 mm 40 mm Determine the mass moment of inertia of the assembly with respect to the z axis. The mass moment of inertia of the assembly with respect to the z axis is x 10-3 kg-m².arrow_forward
- Determine the transferred moment of inertia of Triangle on its Upper vertex when its dimension area B=300mm and H = 600mm. answers in 3 decimal places and in 10410 mm^4.arrow_forward1. (10 points) A thin plate of mass m was cut in the shape of a parallelogram as shown. Determine the mass moment of inertia of the plate with respect to the y -axis. Please simplify your answer as much as possible. A B'arrow_forwardTwo 20-mm steel plates are welded to a rolled S section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal x and y axes.arrow_forward
- The figure shown is formed of 1.5-mm-diameter aluminum wire. Knowing that the density of aluminum is 2800 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure.arrow_forwardBy the method of this article, determine the moments of inertia about the x-and y-axes of the trapezoidal area. 1.4b 1.4b 0.9b b Answers: i bearrow_forward2. A rectangular prism (brick) has dimensions a (in x) b (in y) and c (in z) directions. Taking the origin at the center determine the mass moment of inertia about the y axis in terms of total mass m.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY