Concept explainers
Determine by direct integration the moments of inertia of the shaded area with respect to the x and y axes.
Fig. P9.185
Find the moment of inertia of the shaded area with respect to x and y axes.
Answer to Problem 9.185RP
The moment of inertia of the shaded area with respect to x axes is
The moment of inertia of the shaded area with respect to y axes is
Explanation of Solution
Given information:
The curve Equation is
Calculation:
Sketch the shaded portion with vertical strip as shown in Figure 1.
Refer to Figure 1.
Write the curve Equation as shown below:
Determine the moment of inertia
Substitute
Integrate Equation (3) with respect to x.
Thus, the moment of inertia of the shaded area with respect to x axes is
Determine the area of the strip element
Determine the moment of inertia
Integrate Equation (4) with respect to y.
Thus, the moment of inertia of the shaded area with respect to y axes is
Want to see more full solutions like this?
Chapter 9 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
- Considering L = 50 + a + 2·b + c {mm}, determine the centroidal coordinate Ycg (location of the x´ axis of the centroid) and the moment of inertia is relative to the X´ axis (IX' , ). Assume a minimum precision of 6 significant figures and present the results of the moments of inertia in scientific notation (1.23456·10n ). (Knowing that a=7, b=1, and c=1.) Ycg = IX, =arrow_forwardA channel and a plate are welded together as shown to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes.arrow_forwardA farmer constructs a trough by welding a rectangular piece of 2-mm-thick sheet steel to half of a steel drum. Knowing that the density of steel is 7850 kg/m3 and that the thickness of the walls of the drum is 1.8 mm, determine the mass moment of inertia of the trough with respect to each of the coordinate axes. Neglect the mass of the welds.arrow_forward
- Determine the moment of inertia and radius of gyration of the shaded area shown with respect to the x axis.Fig. P9.9arrow_forwardFor the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia.The L152 × 102 × 12.7-mm angle cross section of Prob. 9.78(Reference to Problem 9.78):Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.arrow_forwardIt 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_forward
- Two L4 x 4 x 1/2-in angles are welded to a steel plate as shown. Determine the moments of inertia of the combined section with respect to centroidal axes respectively parallel and perpendicular to the plate.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_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
- Determine the moment of inertia (in4) Ix of the area shown with respect to the horizontal line that passes to the centroid of the composite area if b= 6.11 in, h= 0.72 in, L= 8.39 in, and W = 0.77 in. Round off only on the final answer expressed in 3 decimal places.arrow_forwardA thin steel wire is bent into the shape shown. Denoting the mass per unit length of the wire by m’, determine by direct integration the mass moment of inertia of the wire with respect to each of the coordinate axes.arrow_forwardDetermine the shaded area and its moment of inertia with respect to the centroidal axis parallel to AA, knowing that d1 = 25 mm and d2 = 10 mm and that its moments of inertia with respect to AA' and BB' are 2.2 × 106 mm4 and 4x 106 mm4, respectively.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