The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labeled edges. The wedge has a = 6, b=9, and c = 6. The solid has constant density 8 = 1. The square of the distance from a typical point (x,y,z) of the wedge to the line L: z = 0, y = 9 is r² =(y - 9)² + z². Calculate the moment of inertia of the wedge about L.

The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labeled edges. The wedge has a = 6, b=9, and c = 6. The solid has constant density 8 = 1. The square of the distance from a typical point (x,y,z) of the wedge to the line L: z = 0, y = 9 is r² =(y - 9)² + z². Calculate the moment of inertia of the wedge about L.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 5. Consider the disk with a rectangular cutout shown in the figure below. The disk has the…

A: Given: The thickness of the disc, t = 3 m The density of the disc, d = 4000 kg/m3

Q: =√x² + y² and above by the plane z = 1. Find the center of mass and the moment of inertia about the…

A: Given:A solid is bounded by and above the plane .The density is .Formula used:The expression for…

Q: show complete solution and complete fbd

Q: Find the centroid of the area bounded by the function f(x) = 1+ sin(x) and the x-axis and the lines…

A: The given function is given by, f(x)=y=1+sinx At x=1, y=1+sin1=1+sin1×180π=1.841 m At x=3,…

Q: A C-section is made up of three rectangles as shown in Figure. Find (i) The centroid of a section…

A: Let us divide the given C -section into three parts of area A1, A2 and A3 Also taking O as origin,…

Q: L y Find the moment of inertia of the shaded area about the x-axis and y-axis, given: y? = x² and…

A: Area moment of inertia about an axis is actually second moment of area about that axis. If "dA" is…

Q: Calculate the moment of inertia of the figure about the X and Y axis

Q: For the shaded area shown, find: (a) The location of the centroid (X,Y). (b) The moment of inertia…

A: (a) Draw the given diagram.

Q: Find the moment finertia about the x-axis of a thin plate bounded by the parabola x = 7y - 3y² and…

Q: Don't Use Chat GPT Will Upvote And Give Handwritten Solution Please

Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

The coordinate axes in the figure run through the
centroid of a solid wedge parallel to the labeled edges.
The wedge has a = 6, b = 9, and c = 6. The solid has
constant density 8 = 1. The square of the distance from a
typical point (x,y,z) of the wedge to the line L: z = 0, y = 9
is r² =(y - 9)² + z².
Calculate the moment of inertia of the wedge about L.
um
G/N
Centroid
at (0, 0,0)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Moment of inertia to be determined:

VIEW

Step 2: Explanation for Moment of inertia:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

13 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD using the coordinate set (x, y, z) in the figure. The dimensions of the wire are a = 24 cm, b = 36 cm. The coordinates of the AB part of the homogeneous wire in the x, y and z axes are given in the following:A) (36; 12; 0)B) (36; 24; 0)C) (36; 24; 12)D) (18; 12; 0)E) (36; 12; 24)
Find the moment of inertia for the cross-sectional shape about the x and y axes, given the function: y = 3·x2 and L = 2 mm.
PROBLEM 4: The region is symmetric about the x-axis. Calculate the moment of inertial about the centroidal x and y axes. ANS: 1x = 10.35 × 106 mm², I₁ = 1.74 × 106 mm² 17 mm y 68 mm 17'mm 18 mm 27 mm x
L3 X = Number y = Number L6 Z = Number 4₁ Find the center of mass (x, y, z) of the object shown, given: L₁ = 120 mm, L2= 90 mm, L3= 25 mm, L4 = 25 mm, L5 = 30 mm, L6 = 20 mm, L7 = Ø 20 mm mm mm LA mm -L7 5 L₂
can ypu please find solution for this question and get back the solution in 30 minutes
1. A circular disk has a density p(r) which varies as a function of distance from the center of the disk. The disk has a radius R and a thickness t. Assuming p(r) = Po(1-r/R): Calculate the total mass of the disk. a. b. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point G. C. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point O. G R
29 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the figure by using the coordinate set. The dimensions of the wire are a= 24 cm, b= 36 cm. In which of the following options are the coordinates of the AB part of the homogeneous wire in the x, y and z axes given correctly?A) (36 ; 24 ; 12)B) (18 ; 12 ; 0)C) (36 ; 12 ; 0)D) (36 ; 24 ; 0)E) (36 ; 12 ; 24)
A shaft is composed of elements made of S355 with a modulus of elasticity of 2.1×1052.1×105 N/mm² and a Poisson's ratio of 0.3. As shown in the picture, on the right side, there are two forces of 10,000 N each, acting at an angle of 15° upwards, creating a moment that is statically compensated by the force F2 on the left side. The shaft is supported at positions A and B. In the same position (for simplicity), there are two critical cross-sections leading to stress concentrations. The sleeve near F2 is shrink-fitted. The dimensions there are d=50 mm, D=120 mm, and the length of the sleeve is 50 mm. Ha=1 µm and Hn=1 µm. The fit is H7/s6. Determine breell.
Use 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.
Problem -05 Moment of InertiaDetermine by direct integration the moment of inertia of the shaded area(Fig -5) with respect to the y axis.
Determine the moment of inertia with respect to the x-axis for the shaded area shown (Figure 2). The dimension is a = 1.00 m.
Find the moment of inertia for the cross-sectional shape about the x and y axes, given the function: y = 2·x2 and L = 1.6 m.