Answered: f you know a rigid body’s moment of…

f you know a rigid body’s moment of inertia about an axis through the center of mass, how do you calculate the moment of inertia for the axis parallel to the center of mass?

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 9.80RP

See similar textbooks

Related questions

Q: For the composite object in the figure; Determine the position of the principal axes and the values…

A: Consider the section as shown below, Calculating moment of inertia about x-axis, Ix1=4412=21.333…

Q: The mass of the displayed object is 10 kg. Its moment of inertia with respect to Lyes of 10 kg-m2.…

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

A: Given question is

Q: Locate the centroid of the cross-sectional área. B. Determine the moments of inertia and the product…

A: As, per the guidelines, I can solve only first three subparts. For rest parts, repost in a separate…

Q: computation of moment of inertia.

A: The moment of inertia of the structure needs to be calculated

Q: What is principal moments of inertia?

A: The general word ‘Moment of inertia’ is used in two contexts, First in place of the second moment of…

Q: What is the triangle’s moment of inertia about an axis perpendicular to the screen and passing…

A: Given data: s=89 mmm=0.4 kg/m Need to determine the moment of inertia about point O and G.

Q: If the diameter of a column is 2.5 cm then the moment of inertia value is given by mm

Q: The principal moments of inertia are always positive. O True O False

A: Moment of inertia is calculated using I=m x r2 m=mass of element & r= distance of mass element…

Q: A wheel has a string of length 4m wrapped round its shaft. The string is pulled with a constant…

Q: 15. Find the principal moments of inertia about the center of mass of a flat rigid body in the shape…

A: The principle axes are…

Q: Why the moment of inertia is always a positive quantity?

A: The moment of inertia is defined as : Here m is the mass in kg And k is the radius of gyration in…

Q: If le is the mass moment of inertia of a rigid body with respect to an axis passing through its…

Q: 2. Find the moment of inertia, radii of gyration and product of inertia considering the figure lies…

A: According to the question, we have to consider only first quadrant. So, the area of the first…

Q: wheel with a mass of 20 kg and a radius of inertia of 300mm, moves under the influence of a torque…

Q: What are the maximum and minimum values of the principal moment of inertia (Imax =?, Imin =?)

A: The moment of inertia about x-axis, Ixx=1220312-12-2×28312=7658.667 cm4

Q: Explain the Concept of the center of gravity, center of mass, and centroid mass moment of inertia.

A: the Concept of the centre of gravity, centre of mass, and centroid mass moment of inertia.

Q: Identify the following statement that is true regarding products of inertia. Product of inertia…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: What is the polar moment of inertia and the corresponding radius of gyration ko

Q: Determine the mass moments of inertia and the radii of gyration of the steel machine element shown…

Q: A flywheel is attached to an engine to keep its rotational speed between 100 rad/s and 110 rad/s. If…

A: Given, Fluctuation of energy = ΔE = 1.05 kJ = 1050 J Maximum rotational speed = ωmax = 110 rad/s…

Q: Date Find the MOVEMENT OF INERTIA about eentroidal x-axis and centroidal y-aric af egiven Figure

A: Before to calculate moment of Inertia, we have to calculate centroid of the given figure.Since,…

Q: The mass moment of inertia of an object 'm' about its CG is Jeg. What is the object's mass moment of…

A: The mass moment of inertia of an object m about the center of gravity is Jcg

Q: Given the theoretical expression for moment of inertia of a point mass, Im=MR2 what is the slope and…

A: a theoretical expression for moment of inertia of a point mass, Im=MR2 now plotting log Im vs log R…

Q: What is the moment of inertia with respect to the xy direction (Ixy) ?

A: Given object is divided into 2 parts. To find centroid (C) position: Part Area (cm2) x y Ax Ay…

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: B. MOMENT OF INERTIA Direction: Solve the following problems related to Moment of Inertia. Show your…

Q: Find the moment of inertia (in mm4) of the shaded area with respect to the yaxis. Round off only on…

Q: A ball has a radius of 1.25 in. and a weight of 0.5 lbs. Find the mass moment of inertia (in…

Q: The product of inertia of area with respect to x-y axes: O Is always positive. O is always zero. Can…

A: Product of inertia The product of inertia of a plane area is defined by following integralsIxy=∫xydA…

Q: Fill in the blanks 1 The polar moment of inertia is equal to moments of inertia about x and y аxes.…

Q: Activity 1. Find the polar moment of Inertia of two circles each with radius r with respect to their…

A: The polar moment of inertia of the circular cross-section about their centroid can be expressed as,…

Q: The moment of inertia of a planet revolving around a star is treated like a point mass. Using the…

Q: 1) Find the moment of inertia applying the parallel axes theorem or steiner's theorem 2) Calculate…

Q: Figure Q8 shows the shaded area with the equation given. Calculate: y? = h Figure Q8 a) the moment…

Q: D moment of inertia circle area: PK =1 #

A: Given

Q: Find the moment of inertia with respect to y-axis the area bounded by x2-4y+8=0, the lines x=0 and…

A: The mathematical expression for calculating the area moment of inertia of an area about the y axis…

Q: Find the moments of inertia Ix ,Iy and Ixy Find the moment of inertia passing through the center of…

A: First we have to locate the center of gravity or centroid of this figure. Then figure out the MOI

Q: Solve the moment of inertia of a point mass that weighs 0.5 kg and has a radius of 5.12 m. The point…

Q: When does the moment of inertia of a cylinder of a certain thickness (A) hollow become equal to the…

Q: What are the difference between first moment of inertia and second moment of inertia and why we…

A: The first moment of inertia is the Mass Moment of Inertia and it is evaluated by multiplying the…

Q: moments of inertia along the x and y axis and radius of gyration

A: Given Shaded region To find Moment of inertia Radius of gyration

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: Find the moment of inertia with respect to the line x=2a the area bounded by x = a2/3 y1/3, the line…

A: To find moment of inertia about x axis

Q: 4) The mass of the homogeneous thin metal plate is 65.0 kg. a) Find the coordinates of the center of…

A: A moment of inertia is a mass of the body when a body is rotating on an axis. The moment of inertia…

Q: How does moment of inertia/parallel axis theorem affect engineering design?

A: Given:- Moment of inertia To find:- Significance in engineering design

Q: What is the moment of inertia of an area?

A: Moment of inertia of an area

Q: What is the relation between moment of inertia and angular velocity?

A: The notation for the moment of inertia is I. And, the notations for the angular velocity is ω. The…

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

If you know a rigid body’s moment of inertia about an axis through the center of mass, how do you calculate the moment of inertia for the axis
parallel to the center of mass?

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

The product of inertia of triangle (a) with respect to its centroid is Ixy=b2h2/72. What is Ixy for triangles (b)-(d)? (Hint: Investigate the signs in the expression Ixy=IxyAxy.)
Using Ix and Iu from Table 9.2, determine the moment of inertia of the circular sector about the OB-axis. Check your result for =45 with that given for a quarter circle in Table 9.2.
Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.
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
The moment of inertia of a planet revolving around a star is treated like a point mass. Using the parallel-axis theorem show that this is a reasonable technique.
Does the moment of inertia change with respect to the reference point?
The mass of the homogeneous thin metal plate is 108 kg. 1. Find the coordinates of the center of mass. 2. Find the mass moment of inertia about the z-axis. 3. Find the mass moment of inertia parallel to the z-axis, but going through the center of mass.Don't forget to include the units for everything.
A thin plate is shown below and it is composed of a square plate which has a mass of 102 kg and a quarter circle plate which has mass 60 kg.1) Find the mass moment of inertia of ONLY THE SQUARE PLATE about the y-axis (Imagine there is no quarter circle plate yet). 2) Find the mass moment of inertia of the entire shape about the x-axis. 3) Find the mass moment of inertia of the entire shape about the y-axis. Show complete solutions please, I want to learn how to solve these items.
A ball has a radius of 1.25 in. and a weight of 0.5 lbs. Find the mass moment of inertia (in ft-lbs-s²) about its center of gravity. The correct answer is 0.0000674
Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2)
If we know the Moment of Inertia of a body about an axis and want to know its moment of inertia about an axis parallel to the first axis, which theorem will be applied? Write down its equation and explain its each term.
Compare the following using brief explanations, illustrations, and mathematical equations: Inertia and Moment of Inertia Thank you ?