Concept explainers
Determine the moment of inertia of the thin ring about the z axis. The ring has a mass m.
Answer to Problem 84P
The moment of inertia of the thin ring about the z-axis is
Explanation of Solution
Given:
The radius of the ring is
The mass of the ring is
Explanation:
Show the intersection of the ring at the arbitrary point
Conclusion:
From Figure 1,
Calculate the mass of the ring.
Here, the density of the material is
Substitute
Here, the density of the material is
Calculate the density of the material from the Equation (II).
Compute the moment of inertia about the
Substitute
Hence, the moment of inertia of the thin ring about the z-axis is
Want to see more full solutions like this?
Chapter 10 Solutions
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
- Determine the moment of inertia about the y-axis of the shaded area of the figure shown:*arrow_forwardDetermine the moment of inertia and the radius of gyration of the shaded area with respect to the x-axis. Given: r = 79 mm. 125 mm 125 mm - 250 mm The moment of inertia is The radius of gyration is *106 mm4. mm.arrow_forwardDetermine the moment of inertia and the radius of gyration of the shaded area shown with respect to the x axis.arrow_forward
- Determine the moment of inertia of the solid steel assembly about the x-axis. The specific weight of steel is Yst = 488 lb/ft3. 0.25 pie -2 pies- 3 pies ļ 0.5 pie Xarrow_forwardDetermine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point O. -0.80h Answers: lx = i ly= i lo = i 0.67h -0.80h h4 h4 h4arrow_forwardDetermine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point O. -0.56h Answers: 1x = i ly= i lo= i 0.60h -0.56h h h4 h4 hearrow_forward
- Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the y axis.arrow_forwardFormulas Moments of Inertia x= [y²d ly = fx²dA Theorem of Parallel Axis Ixr = 1 + d² A * axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between x and x' ly₁ = 15+d²A ỹ axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1=Σ 4 All the moments of inertia should be about the same axis. Radius of Gyration k=arrow_forwardDetermine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/m³. 0.10m AY 0.30m 0.10m 0.60m 0.05m 0.20m Z. 0.10 0.40marrow_forward
- Determine the moments of inertia about the y-axis of the circular area without and with the central square hole. R Answers: 1.3R With hole +1.3R Without hole ly= i R4 R4arrow_forwardFind the moment of inertia of a triangular section having 50 mm base and 60 mm height about an axis through its centre of gravity and base. Answer :IG = 300 x 103 mm4; IBase = 900 x 103 mm4arrow_forwardThe homogeneous plate of Prob. B/7 is repeated here. Determine the product of inertia for the plate about the x-y axes. The plate has mass m and uni- form thickness t. x = ky² B/7 For the thin homogeneous plate of uniform thickness t and mass m, determine the mass moments of inertia about the x'-, y'-, and z'-axes through the end of the plate at A. Refer to the results of Sample Problem B/4 and Table D/3 in Appendix D as needed. x = ky² Thickness t Problem B/7arrow_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