PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 10, Problem 9P
Determine the moment of inertia of tire area about the x axis. Solve the problem in two ways, using rectangular differential elements, (a) having a thickness dx and (b) having a thickness of dy.
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Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = 7y - 3y² and the line x + 2y = 0 if 8(x,y) = x + 2y.
Choose the correct sketch of the plate described above.
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O A. SS F(x,y) dy dx
O B.
OB. F(x,y) dx dy
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Select the order of integration that will make the computations easier and fill in the limits of integration in your choice.
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O C.
O D.
Use the given density function 8 to write the appropriate integrand F(x,y) for finding the moment of inertia. Then substitute into the correct integral from the previous step and evaluate to find the moment of inertia for the plate.
The moment of inertia is
(Simplify your answer.)
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Q1/ Find the polar moment of inertia of the shaded area. I need solution
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Determine the moment of inertia of the area about the x
axis. Solve the problem in two ways, using rectangular
differential elements: (a) having a thickness dx and
(b) having a thickness of dy.
Chapter 10 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 10 - Determine the moment of inertia of the shaded area...Ch. 10 - Determine the moment of inertia of the shaded area...Ch. 10 - Determine the moment of inertia of the shaded area...Ch. 10 - Determine the moment of inertia of the shaded area...Ch. 10 - Determine the moment of inertia of tire area about...Ch. 10 - Prob. 13PCh. 10 - Prob. 21PCh. 10 - Determine the moment of inertia of the beams...Ch. 10 - Prob. 6FPCh. 10 - Prob. 7FP
Ch. 10 - Prob. 8FPCh. 10 - Determine the moment of inertia of the composite...Ch. 10 - Determine the moment of inertia of the composite...Ch. 10 - Prob. 29PCh. 10 - Determine the moment of inertia for the beams...Ch. 10 - Determine the moment of inertia for the beams...Ch. 10 - Prob. 36PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 50PCh. 10 - Determine the moment of inertia for the beams...Ch. 10 - Prob. 52PCh. 10 - Prob. 53PCh. 10 - Prob. 54PCh. 10 - Prob. 57PCh. 10 - Prob. 58PCh. 10 - Prob. 66PCh. 10 - Prob. 67PCh. 10 - Prob. 84PCh. 10 - Prob. 85PCh. 10 - Prob. 87PCh. 10 - Determine the moment of inertia of the homogenous...Ch. 10 - Determine the moment of inertia of the...Ch. 10 - Prob. 90PCh. 10 - The concrete shape is formed by rotating the...Ch. 10 - The right circular cone is formed by revolving the...Ch. 10 - The pendulum consists of a 8-kg circular disk A, a...Ch. 10 - Determine the moment of inertia Ix of the frustum...Ch. 10 - Prob. 100PCh. 10 - Prob. 101PCh. 10 - Prob. 103PCh. 10 - Prob. 104PCh. 10 - Prob. 105PCh. 10 - Prob. 106PCh. 10 - Prob. 107PCh. 10 - Prob. 108PCh. 10 - Prob. 109PCh. 10 - Prob. 5RP
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- Find 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_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_forwardCalculate the Moment of Inertia of the given lamina, for the dimensions B=20mm, D=30mm, b=15mm and d=25mm. y A B E C.G X - X d D H D b Barrow_forward
- Define The moment of inertia and determine it for T-sectionarrow_forwardProblem Statement Based on Problems 10-19/20 from the textbook. Determine the moment of inertia of the area about: a) the x-axis b) the y-axis Hint: See Appendix A for common integral solutions. a=4.5ft y=a-2arrow_forwardQ2: Determine the moment of inertia of the area about the x – axis. Solve the problem in two ways, using rectangular differential elements: (a) having a thickness of dx, and (b) having a thickness of dy. -y = 4 - 4x2 4 in. 1 in. 1 in.arrow_forward
- Find the Moment of inertia of the given section about X-X axis passing through its center of gravity. Take A= 80 mm, B= 20 mm, C= 60 mm and D= 100 mm A B .C Darrow_forwardUse the given values in problem to answer the following: Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar. The dimensions of the section are: l=51 mm, h=29 mm The triangle: hT=15 mm, lT=18 mm and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.arrow_forwardANSWER THE FOLLOWING CORRECTLY AND PROVIDE A DETAILED SOLUTION. 1. DETERMINE THE MOMENT OF INERTIA OF THE SHADED SECTION ABOUT THE GIVEN X-AXIS.arrow_forward
- Determine the moments of inertia about the y-axis of the circular area without and with the central square hole. 1.2R R +1.2R Answers: Without hole ly= i R4 With hole ly= i R4arrow_forwardCalculate the moment of inertia of the shaded area about thex-axis. 90 mm |30 mm - 45 mm -45 mm Answer: Ix = (106) mm4arrow_forwardDetermine the moment of inertia of the area under the curve about the x-axis (Ix) from 0 <= x <= 1 of the function: y=x3 graph the functionarrow_forward
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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY