Answered: The distance from an axis at which the…

The distance from an axis at which the mass of a body may be assumed to be concentrated and at which the moment of inertia will be equal to the moment of inertia of the actual mass about the axis.

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: A hollow cylinder and a solid cylinder have the same diameter. Determine which has the greater…

Q: 100 mm Problem (3) A 3-mm thick piece of aluminum sheet metal is cut and bent into the machine…

A: mass od all the sections m1 = ρV1 = 2270×(0.24×0.18×0.003) = 0.294 kgm2 = ρV2 =…

Q: A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that…

A: Given that, Diving the sheet into two section as shown below –

Q: 9 cm 15 cm

Q: A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the…

A: From the given figure it is clear that the sheet consists of three surfaces, one semicircular…

Q: The figure shown is formed of 1.5-mm-diameter aluminum wire. Knowing that the density of aluminum is…

A: Draw the schematic diagram for a clear understanding of the above problem.

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

A: Solution : The mass is calculated as:

Q: The area shown is revolved about the x axis to form a homogeneous solid of revolution of mass m .…

A: Given Revolution mass = m To find in terms of m The mass moment of inertia about X axis Y axis

Q: A uniform circular disk 3ft in diameter weighs 960lb. what is its moment of inertia abouti ts usual…

A: Given: m = 960 lb r = 3ft

Q: A small connecting rod 220 mm long between centres, is of 2 kg mass and has a moment of inertia of…

A: The answer is

Q: The radius of gyration is: O The same as the distance of the centroid of an area from an axis. O One…

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

Q: . The thin plate shown is composed of a rectangular plate of mass 102 kg and a quarter-circular…

Q: From the figure shown below, the mass of the rectangular prism is 50 kgs, mass of rod is is 10 kgs…

A: The mass moment of inertia of the cuboid about the y axis can be determined as,

Q: Consider a cube with mass m and side a. (a) Show that the ellipsoid of inertia at the center of the…

Q: The homogeneous circular cone shown has a mass m . Determine the mass moment of inertia of the cone…

Q: . Which of the following statements are true of moment of inertia? a) For a given body (e.g., a…

A: The question with correct lettering of option is given below 1. Which of the following statements…

Q: A thin, semielliptical plate has a mass m . Determine the mass moment of inertia of the plate with…

A: Given data: *The mass of the semi elliptical plate is m. Let the thickness of the plate be t. Thus,…

Q: CS South-line. Consider a sphere with radius R and mass M. Assuming that the moment of inertia of…

Q: From a circular disc of mass M and radius Ra circular portion of radius R/2 is removed as shown in…

A: As per the given conditions, the disk must touch the outer boundry and also the center of the disk…

Q: determine the mass moment of inertia of steel balls used in ball bearings. Use a diameter of 2cm

A: Given that diameter of steel ball is 2 cm

Q: A 8 lb metal sheet lies on xy-plane. Given that the length a=7 in and the centroid of the metal…

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: For the the mass of flywheel of an engine is 6.5 tonnes and the radius of gyration is 1.5…

A: here given that, Mass (M) = 6.5 tonnes = 6500 kg. Radius of gyration (K) = 1.5 m. I = ?

Q: OD = 150 mm 1400 mm Determine (to two decimal places) the mass moment of inertia (in kg.m2) of the…

Q: The mass moment of inertia of a thin ring of mass m and radius R about the z axis is O A. (1/4) mR2…

A: The mass moment of inertia of a rhin ring of mass m and radius R about x or y axis =mR2/2

Q: find the polar moment of inertia of thin triangular plate a bounded by the line y = x, y=-x and y =…

A: Given lines are y=x y=-x and y=1 if (x,y) = y+1 kg m2

Q: How can the moment of inertia of a body can be determined?

A: The instantaneous center of rotation is defined as the point on a body about which a body rotates at…

Q: A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the…

A: a= 100 mm b= 120 mm c= 200 mm ρ= 7850 kg/m3 let's assume small element inside cube with sides of dx,…

Q: For the rectangular prism shown, determine the values of the ratios b/a and c/a so that the…

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: Show that the principal moments of inertia of any rigid body satisfy I3 ≤I1 +I2. For what shape of…

A: The moment of inertia of a body (area or mass) about a line is the sum of the products formed by…

Q: The thin plate shown is composed of a rectangular plate of mass 102 kg and a quarter-circular plate…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the…

A: Given data: b=h=10 cm Need to determine the moment of inertia of the triangular area relative to a…

Q: 72. From a solid sphere of mass Ma hollow sphere of radius is removed. Moment of inertia of…

Q: A flywheel in the form of a uniform disk 4 ft in diameter weighs 600 lbs. What is its rotational…

A: Diameter of a disk, D=4 ftWeight of the disk, W=600 lbs

Q: For the shown vibratory mechanical system he mass moment of inertia of the rotating disk R. 3mR…

A: R = 140 cm m = 70 kg k = 3500 N/m Mo = 1750 Nm

Q: The mass distribution of a 3 dimensional rigid body is characterized by the Principal moment of…

A: The tensor of Moment of inertia defines the characterized of the Mass distribution analogously.

Q: What is the moment of inertia of the system below: (Consider the mass of the connections to be zero)…

Q: OD = 150 mm %3D 1400 mm Determine (to two decimal places) the mass moment of inertia (in kg.m2) of…

A: For the given part thickness (t) = 60 mm density of part (ρ)= 25 kg/m3 To determine The mass…

Q: Given an arbitrary body and three rectangular axes x, y, and z,, prove that the mass moment of…

A: Given: An arbitrary body three rectangular axes x, y, and z To prove: Ix ≤ Iy +Iz Iy ≥ 1/2Ix

Q: determine the centroidal polar moment of inertia of a rectangle 100mm wide by 200 mm high

A: Given:- h=200mm b=100mm To find:- Polar moment of inertia about centroidal axis

Q: The mass moment of inertia of a thin ring of mass m and radius R about the Z axis is m R2 (1/4) a O…

A: Moment of inertia: It is a measure of how a body changes in its rotational motion under the action…

Q: For the multi shapes, the moment of inertia is ................. to the algebraic sum of the moments…

A: For the multi shapes, the moment of inertia is .......... to the algebraic sum of the moments of…

Q: A thin, rectangular plate with a mass m is welded to a vertical shaft AB as shown. Knowing that the…

Q: Determine (to two decimal places) the mass moment of inertia (in kg.m2) of the system shown above…

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…

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

The distance from an axis at which the mass of a body may be assumed to be concentrated and at which the moment of inertia will
be equal to the moment of inertia of the actual mass about the axis.
A) Radius of Gyration
B Radius of Gyraytion
Diameter of Gyration
Diameter of Gyraytion

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 with 1 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

20 The mass moment of inertia ( Ix) of a sphere of mass 5 kg and radius 25 mm is -------------- a. 1450 mm4 b. 1350 mm4 c. 1250 mm4 d. 1550 mm4
A composite plate is constructed by welding together a 12-kg semicircular plate to a 14-kg rectangular plate as shown.1. Which of the following best approximates the mass moment of inertia of the composite plate about the y-axis? A. 1536 kg-cm^2 B. 581 kg-cm^2 C. 864 kg-cm^2 D. 621 kg-cm^2 2. Which of the following best approximates the radius of gyration of the composite plate about the y-axis? A. 5.76B. 7.69C. 11.56D. 4.72
A homogenous thin plate of mass 2kg and radius r = 3? cm is shown. If d is 4cm, what is the moment of inertia about axis CC’ .
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.
A uniform circular disk 3ft in diameter weighs 960lb. what is its moment of inertia abouti ts usual axis?
If le is the mass moment of inertia of a rigid body with respect to an axis passing through its center of mass, then the mass moment of inertia I of the same body with respect to a parallel axis some distance away from the center of mass
For the figure shown knowing that a = 1.00 cm and b = 4.00 cm, determine:(a) The centroid of the figure shown.b) The moments of inertia Ix and Iy and the product of inertia Ixy about the x and y axes.c) The angle m corresponding to the location of the principal axes.d) For the u-v axes shown and obtained by rotating an angle = 34.0° clockwise, the corresponding momentsand product of inertia using Mohr's circle.
A hollow cylinder and a solid cylinder have the same diameter. Determine which has the greater moment of inertia with respect to an axis of rotation along the axis of the cylinder. (a) when the cylinders have equal mass hollow cylindersolid cylinder (b) when they have equal density solid cylinderhollow cylinder
Determine the mass products of inertia Ixy, Iyz, and Izx of the cast aluminum machine component shown. (The specific weight of aluminum is 0.100 lb/in3.)
Find the moment of inertia of a solid parallelepiped of homogeneous mass density, mass M, and sides of length a, b, and c with respect to: a) One of its principal axes of inertia b) An axis at a distance d from its center and parallel to the previous axis of rotation.
Shown is the cross section of an idler roller. Determine its mass moment of inertia and its radius of gyration with respect to the axis AA ’. (The specific weight of bronze is 0.310 lb/in3 ; of aluminum, 0.100 lb/in3 ; and of neoprene, 0.0452 lb/in3).
Consider a cube with mass m and side a. (a) Show that the ellipsoid of inertia at the center of the cube is a sphere, and use this property to determine the moment of inertia of the cube with respect to one of its diagonals. (b) Show that the ellipsoid of inertia at one of the corners of the cube is an ellipsoid of revolution, and determine the principal moments of inertia of the cube at that point.