Q4: Answer one of the following questions:a. Determine the moments of inertia of the shaded area shown in (Fig. 4-a) withrespect to the x and y axes when a = 20 mm.b. Determine the moments of inertia I, and I, of the area shown in (Fig. 4-b) withrespect to centroidal axes respectively parallel and perpendicular to side AB.A1.2 in.5.0 in.1.8 in.0.9 in.-2.0 in. 2.1 in.Fig. 4-aFig. 4-b

In the strength of material, stress & strain is determined for various material. Stress is the…

Answered: a. Determine the moments of inertia of…

a. Determine the moments of inertia of the shaded area shown in (Fig. 4-a) with respect to the x and y axes when a = 20 mm.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.3P: The moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4,...

See similar textbooks

Related questions

Q: Suppose that a = 140 mm and b = 392 mm . A) Determine the moment of inertia for the shaded area…

Q: By the method of this article, determine the rectangular and polar radii of gyration of the shaded…

A: Write the given data. ro=ari=0.36a

Q: Problem n2. Semicircle O 20mm 20mm 40mm Determine the polar moment of inertia of the bleu area shown…

Q: Q.2. Determine the moment of inertia of the composite area about the x and y axis. 150 mm -150 mm--…

A: find the moment of inertia about x axis and y axis.

Q: Determine the moment of inertia of a rectangle 100cm by 300cm with respect to a line through its…

A: The moment of inertia of a rectangle with respect to a line through its center of gravity and…

Q: Determine the area moment of inertia Ix of shaded area about the x axis. Determine the area moment…

Q: A thin plate with a mass m was cut in the shape of a parallelogram as shown. Determine the mass…

A: We will consider the parallelogram as a square to make our calculation easier. Let's consider this…

Q: A. Determine the moments of inertia of the shaded area about the x-axes and y-axes. 12:16 PM

Q: Determine by direct integration the product of inertia of the given area with respect to the x and y…

A: Let us take a strip of thickness dx at a distance x as shown below, The area of the strip will be,…

Q: Determine the polar moment of inertia and the polar radius of gyration of the rectangle shown with…

A: Given: The height of the rectangle is h=a The width of the rectangle is b=2a

Q: ment of inertia of section shown ir parallel and perpendicular to AR

Q: Suppose that a = 3 in. and b = 7.5 in. Determine the product of inertia for the shaded area with…

A: We have to Determine the product of inertia for the shaded area with respect to the x and y axes.

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: Given Data: The straight line y = mx passes through points (0,0) and (a,b) The parabola y = kx2…

Q: リ=400× Som 2 00 m

Q: The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia…

A: Given that shape is rectangular , Let b be the base and h be the height . Need to find moment of…

Q: A piece of thin, uniform sheet metal is cut to form the machine component shown. Denoting the mass…

A: Given Data: The mass of the component is m. The area of the component can be determined as, Where…

Q: 1B. Derive from first principles the moment of inertia for a right-angled triangle about its base…

A: Consider a right-angle triangle with base b and height h as shown below,

Q: The homogeneous object below has density 7800 kg/m³. Determine its moment of inertia about the axis…

Q: By direct integration, determine the moments of inertia of the triangular area about the x- and…

A: For the triangular area, b = 7 in h = 15 in It is required to determine the moment of inertia of the…

Q: Question 5: For the shaded shown in the figure below, determine the moments of inertia with respect…

A: Mark the number on the I-section to solve the problem part by part as follows: The moment of…

Q: Determine the distance h for which the moment of inertia of the region shown about the x-axis will…

A: Understand that the given figure is divided into three parts for ease of calculation as the moment…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

A: The equation of line is, y = mx The equation of curve is, y = kx2 At x = a, y = b substitute in…

Q: Which of the following is the measure of distribution of the body's mass about the axis about which…

A: Answer :- Radius of gyration

Q: For the shaded area shown, given that a = 14 cm; b a a - t 2а A. Determine the moment of inertia…

A: Given Data a=14 cm b=12 cm t=1.5 cm Shaded area is symmetrical about y-axis then centroid lies on…

Q: By the method of this article, determine the rectangular and polar radii of gyration of the shaded…

Q: a+b -

A: Given, a = 120 mm b = 180 mm r = 80 mm We can consider the given section as combination of below 3…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: The elementary diagram for the shaded area is as follows:

Q: Determine the polar moment of inertia and the polar radius of gyration of the rectangle shown with…

A: In this rectangle E, F, G & H are the midpoints of each side respectively.

Q: A section of sheet steel 0.03 in. thick is cut and bent into the sheet metal machine component…

A: The figure is given as Mass of part 1 m1=γsgV1=γsgA1t=49032.21210.3750.0025=0.007133 lb.s2/ft Mass…

Q: Determine by direct integration the product of inertia of the given area with respect to the x and y…

A: Let us take a strip of thickness dy at a distance y as shown below, The area of the strip will be,…

Q: the ratio moment of inertia of a rectangular shape to triangular shape having the same base width(b)…

A: The moment of Inertia of a plane area with respect to x and y axis respectively is defined by the…

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

A: find the centre of mass and moment of inertia about y-axis.

Q: A thin plate with a mass m is cut in the shape of an equilateral triangle of side a . Determine the…

A: Each side of the given equilateral triangle is a units. →Mass of the…

Q: By the method of this article, determine the moments of inertia about the x-and y-axes of the…

Q: B/34 Determine the moment of inertia about the x-axis of the portion of the homogeneous sphere…

A: It is known that the moment of inertia of a solid sphere is Here, Ro is the radius of the sphere.…

Q: Moment of inertia of square plate about the axis shown is axis M 130°

A: Mass moment of inertia of an area is defined as the product of mass of area and the distances of its…

Q: . The ratio of the moment of inertia of a at of a square plate for equal depth, is (a) less than one…

A: Answer : Width=DDepth=DDiameter=D

Q: Q.2. Determine the moment of inertia of the composite area about the x and y axis. 150 mm -150 mm--…

Q: Determine the area moment of inertia Ix of shaded area about the x axis. Determine the area moment…

Q: Calculate and determine the Moments and Principal Axes of Inertia of the profile below, indicating…

A: Any object's centroid, or centre of gravity, is the place within that object where the force of…

Q: By the method of this article, determine the moments of inertia about the x- and y-axes of the…

A: A trapezoidal area is given below,

Q: 1. Determine the moment of inertia of the above section (Fig. 1) about Ox axis.

Q: 2сm h 2cm b 2сm

A: Center of gravity Center of gravity is a point in a body where all the mass of body is concentrated.…

Q: The moment of inertia with respect to the x and y axis have been computed and are known to be L =…

Q: The directions in degrees of the main axes of inertia of the area presented below are

A: As we can see the given lamina has center of mass C and it is symmetric about x, y and z all axis…

Q: Determine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials…

A: Given: The mass intensity of element, m = 60 kN/m3

Q: h/2 R=3cm h/2 b/2 b/2 9cm b

A: Center of gravity Center of gravity is the point in the body where all the mass of body is…

Q: 100 mm 20 mm Yo 3) Determine the moments of inertia of the Z -section about its centroidal xo - and…

A: Draw the schematic diagram of the Z-section.

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

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

The moment of inertia of the plane region about the x-axis and the centroidal x-axis are Ix=0.35ft4 and Ix=0.08in.4, respectively. Determine the coordinate y of the centroid and the moment of inertia of the region about the u-axis.
The moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4, respectively. Determine y (the y-coordinate of the centroid C) and Ix (the moment of inertia about the centroidal x-axis).
For the entire section shown, the moments of inertia with respect to the centroidal x and y axes at point C are Ix = 0.162(106) mm4 and Iy = 0.454(106) mm4, respectively. a. Determine the product of inertia with respect to the centroid at C, in mm4. b. Use a Mohr's Circle to determine the orientation (in degrees) of the principal axes of the section about the centroid C. c. Use the same Mohr's Circle to determine the values of the principal moments of inertia about the centroid C, in mm4.
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.
Determine the moment of inertia of a rectangle 100cm by 300cm with respect to a line through its center of gravity and parallel to the shorter side.
Prove that the centroidal polar moment of inertia of a given area A cannot be smaller than A2/2π (Hint:Compare the moment of inertia of the given area with the moment of inertia of a circle that has the same area and the same centroid.)
Determine the moment of inertia (cm4) Īx of the area shown with respect to the horizontal line that passes to the centroid of the composite area if a = 5.3 cm, b = 11.9 cm, and c = 6 cm. Round off only on the final answer expressed in 3 decimal places.
Find the Moment of Inertia of the plate as shown in figure, passing through its centroid with reference to Y -Y axis. Where b1 = 55 mm, d1=110 mm, b2=160 mm, d2=30 mm, b3=65mm, d3=24mm. The value of is (unit in mm) = ______________ Answer for part 1 The value of is (unit in mm) = ______________ Answer for part 2 The value of total for the given plate is (unit in mm4) =________________ Answer for part 3
Consider the shaded area shown. Suppose that a = 120 mm , b = 180 mm , and r = 80 mm . Determine the moment of inertia of the shaded area about the x axis. Ix = ?
need asap Determine the moment of inertia (cm4) Īy of the area shown with respect to the vertical line that passes to the centroid of the composite area if a = 4.6 cm, b = 13.4 cm, and c = 6 cm. Round off only on the final answer expressed in 3 decimal places.
For the surface shown in the figure below, determine:a) The xc and yc coordinates of its centroid;b)The moments of inertia and product of inertia in relation to the centroidal axes x' and y' (axes parallel to x and y , which pass through the centroid);c)Using Mohr's circle, the new moments and product of inertia obtained by rotating these centroidal axes by 35° counterclockwise.
The moments and product of inertia of an L4 x 3 x 1/4-in. angle cross section with respect to two rectangular axes x and y through C are, respectively, Ix = 1.33 in4. Iy = 2.75 in4, and Ixy <0, with the minimum value of the moment of inertia of the area with respect to any axis through C being Imim = 0.692 in 4 Using Mohr’s circle, determine (a) the product of inertia Ixy of the area, (b) the orientation of the principal axes, (c) the value of Imax.