5. Calculate the moment of inertia tensor for a uniform triangular sheet of mass M; Cal-culate (a) the components Iap and (b) the components Ip for the rotated coordinatesystem:Answer (a):Answer (b):laß=MP²12laß =MP²12145°2 -1 0-12 000 4100030004

Given A traingular sheet of mass To Findmoment of inertia of sheet

Answered: 5. Calculate the moment of inertia…

5. Calculate the moment of inertia tensor for a uniform triangular sheet of mass M; Cal- culate (a) the components Iaß and (b) the components Ip for the rotated coordinate system: 45° X

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: Derive the mass moment of inertia about the central x-axis of the hemisphere shown below. Assume…

Q: For the body shown. If point P3 is the center of mass for rod part P1-P2, and point P4 is the center…

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

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: Please find the radius of Gyration Kx. The density is 5000 kg/m³ 0.5 m 1 m-

Q: 2. Determine the mass moment of inertia for the following rigid bodies about an axis at its center…

A: Given M= 10 lb Length of bar = 2ft Moment of inertia of bar about O = ML^2/12 M.O.I= (10×2^2)/12…

Q: computation of moment of inertia.

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

Q: show complete solution and complete fbd

Q: 1. Determine the centroidal moment of inertia about X and Y axis.

Q: The definition of the Area moment of Inertia involves integral of the form oSr² dm Ofx² dm O|x dA o…

A: Moment of moment of area (second moment of area ) is known as the area moment of inertia, it shows…

Q: The figure below gives the moment of inertia Io for a point mass rotating about point O. As a…

Q: Determine the moment of inertia a uniform steel disk about an axis perpendicular to the disk and…

A: Given the density, thickness and radius of disk. Required: Moment of inertia about O.

Q: Fine the coomants fot the region.given in the figure about the x and akes

Q: Find the second moment of inertia with respect to the z axis? (a)793cm^4 (b)624 cm^4 (C)1242 cm^4…

A: Moment of inertia: The moment of inertia is calculated by two methods, they are the mass moment of…

Q: Determine the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown. 5…

A: At y = 5 in,z = 15 inTherefore, h = 15 in

Q: Differentiate between the Inertia, Moment of Inertia and Mass Moment of Inertia. Also give at least…

A: The concept of Inertia came from Newton's first law of motion. An object at rest remains at rest, or…

Q: A hollow mast of circular section as shown is to be stiffened by bonding two strips of the same…

Q: Ix, Iy, Ixy 10 cm Y 5 cm 10 cm 5 cm X

Q: Find the mass moment of inertia, Izz, for the spherical ceramic femoral head ball (with a…

A: The radius of the sphere is r, The radius of the cylinder is r/2. The height of the cylinder is…

Q: The moment of inertia of the hollow circular beam with 40 mm outer diameter and 10 mm thickness is

A: Given that outer diameter=40 mm=Do thickness of the hollow circular beam=10 mm= t Now, calculate the…

Q: Examples: Moments of inertia of the pendulum about an axis 1) passing through point O, and 2) mass…

Q: P d L R A square made of aluminum (density p = 2700 k m and has dimension L = 5.20 m and thickness e…

Q: -ху —D 10 5 4 3 1 x(m) 4 6 4 I, = 105 X m" Iy 35 x m4 m %3D =

A: Write the expression for the radius of gyration for both the axis.

Q: =) Find the moment of inertia tensor of a solid hemisphere of mass M and radius R centered at the 글…

Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the y = 2x, and the…

Q: a Z a y

A: To obtain the moment of inertia tensor of the right triangular pyramid about its center of mass…

Q: 600 mm C 360mm

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: 13.9. Calculate the components of a moment of inertia tensor for the following configuration. Point…

Q: Calculate total moment inertia of a lamina if the density is 7780 kg/m3 using theorem of parallel…

Q: of the wheel). The total mass of the wheel is 3.0 kg and 55% of the mass is evenly distributed on…

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: The moments of inertia of the area A about the parallel p- and p' -axes differ by 15*10ʻmm . Compute…

A: Given data Ip-Ip'= 15×106 mm4

Q: y 4.5 3 3.5 45° 10.5 10

Q: A solid cylinder with a radius of 3.9 cm has the same mass as a solid sphere of radius R Part A If…

Q: 2. (a) Use the parallel axis theorem to calculate the inertia tensor for the same thin rectangular…

A: (a) Draw a thin rectangular slab.

Q: a. Locate the coordinates of the centroid. b. Calculate the moments of inertia about the given x and…

A: we will split the shape into three parts, calculate the centroid of the combined shape

Q: 久

Q: X₂ Find the moments of inertia Ix, ly, lo for a lamina that occupies the part of the disk ² + 1² VI…

A: So the radius of the circle will be less than and equal to:We can consider the density as So 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

5. Calculate the moment of inertia tensor for a uniform triangular sheet of mass M; Cal-
culate (a) the components Iap and (b) the components Ip for the rotated coordinate
system:
Answer (a):
Answer (b):
laß
=
MP²
12
laß =
MP²
12
1
45°
2 -1 0
-1
2 0
0
0 4
100
030
004

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: Given data

VIEW

Step 2: I_XX, I_YY calculation

VIEW

Step 3: I_XY, I_ZZ calculation

VIEW

Step 4: I' calculation

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 10 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

I need the answer as soon as possible
Q.2) Explain Reynold’s number based on viscous and inertia forces
2
Will upvote!
Problem -05 Moment of InertiaDetermine by direct integration the moment of inertia of the shaded area(Fig -5) with respect to the y axis.
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) * k1 Jo- k2 m2
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=55 mm, h=22 mm The triangle: hT=12 mm, lT=19 mm and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 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? Enter the y position of the center of gravity of the bar in mm with one decimal.
In civil construction it is very common to use L sections, angle, for comer pillars. Calculate the center of gravity L drawn below, informing the x coordinates with respect to the y axes and the Moment of Inertia Ix and Iy with respect to this center of gravity. Consider as measurements in centimeters, where: = 60 b= 90 Note: use Steiner's theorem 50 a 20
Moment of inertia of a square about its centroidal axis decreases with decrease in side of the square. Justify this statement with your own example.
4 cm -10 cm Calculate the moment of inertia l, in the coordinate set (x,y) placed at the center of gravity of the section given 4 cm 10 om M in the figure. Write the result by rounding to the nearest whole number and specifying the unit. y5.5 cm
Answer neatly with a complete solution.
with integration. find mass moment of inertia as well as radius of gyration of uniform thin parabolic plate about x and y axis. plate has mass per unit area p= 2kg/m^2