Problem 3: The inertia matrix can be written in dyadic form which is particularly usefulwhen inertia information is required in various vector bases. On the next page is a rightrectangular pyramid of total mass m. Note the location of point Q.(a) Determine the inertia dyadic for the pyramid P, relative to point Q, i.e., 7%, for unitvectors ₁₁, 2, 3. 5822h/c.m.)k12/2hhQRight rectangular pyramid

Answered: Image /qna-images/answer/8fef98d7-c373-4622-a0b8-110f6aa9f597.jpg

Answered: Problem 3: The inertia matrix can be…

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 9.87RP

See similar textbooks

Similar questions

" POLAR MOMENT OF INERTIA " Please refer to the answer key (book from Engineering Mechanics by SInger) Please include the analyzation of figure so that i could undestand the steps and solution. Thankyou!
Ip Given: Plate's radius: r_P= 80mm Hole's radius: r h= 22mm Plate's constant density p = 8950 kg/ m Plate's thickness: t= 1cm Find: The moment of inertia about an axis passing through point P
6. Derive an expression for the moment of inertia of the pictured semi- circular loop-rod device about an axis through the point P, perpen- dicular to the page. The mass of the semicircular loop is 3.14 kg, and the rod is 3.0 kg. Take R = 1.0 m. [24.14 kg m²] 3R
The mass moment of inertia I of a homogeneous sphere about its diameteris I = (2/5)m R², where m and R are its mass and radius, respectively. Find thedimension of I in terms of the base dimensions of (a) a gravitational [FLT] systemand (b) an absolute [MLT] system.
Match the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: ris distance, m is a mass, k is a radius of gyration and d is a distance from the mass moment of inertia IG about the center of mass A. D. O M X Mass element Z Rotation axis X A.1=1+md² G B. = SM √² r²dm C.I=mk²_ D.1= Σm,r?
A disk attached with a shaft AB, which both end of the shaft have base support, as shown in figure 1 below. Determine the moment of inertia of the disk about the axis of shaft AB.The disk has a mass of 20kg
Two balls of mass ma and m, are connected by a massless rod of length L. The two vertical dashed lines in the figure, below, represent two different axes of rotation (axes a and b). These axes are parallel to each other and perpendicular to the rod. If the ratio between the two moments of inertia, as measured relative to each axis, is 4 = 3. Ib a. Find the ratio of the masses (ma/mp). b. Find the distance from ball a to the system's center of mass. Axis a Axis b L- ma Two balls connected by a massless rod of length L rotate around the two axes shown.
For a given non-symmetric area and origin, when plotting Mohr's Circle, a reference point doesn't lie on the circumference but is located at the average distance between Imax and Imin at (297, 0). This reference point is the center of Mohr's Circle must correspond to one of the two principal moments of inertia corresponds to an axis on the cross-section that is not principal O provides the radius of Mohr's Circle that is equal to 297 provides the diameter of Mohr's Circle that is equal to 297
Complete the following sentence 1- The center of mass of a rigid body in the form of thin wire across y-direction is given by.. 2- The center of mass of a rigid body in the form of thin shell across x-direction is given by. . 3- The moment of inertia of a rigid body rotate about a fixed axis (z- axis ) is given by.. . 4- The rotational kinetic energy of a rigid body rotate about a fixed axis is given by. . 5- The torque about the axis of rotation is given by.... .....................
Consider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame are represented by N-frame and B-frame, where {^₁, ñ2, ñ3} and {b₁, 62, 63} are right-handed vector bases fixed in N-frame and B-frame, respectively. {b} is aligned with the principal axis of inertia, where 6₁ and 63 are associated with the minimum and maximum moments of inertia, respectively. Denote the satellite angular velocity by w = wibį and the inertia tensor about the CoM by Ie. Suppose that I at time t = 0 is given by: Ic(t = 0) = 2ñ₁ñ₁ +2.25 ñ₂n₂ +2.25 ñ3ñ3 -0.75 n₂n3 -0.75 n3n2 (dimensionless) (a): First, let us characterize the inertia property of the satellite from the given information. (a.1): Express the satellite inertia tensor about the CoM in B-frame. Sketch the inertia ellipsoid of this body with B-frame.
Question 9: Figure 3 shows a mechanical system. The rod (with moment of inertia J) rotates about the pivot at only small rotation angles. As pictured, theta is positive clockwise. Attached is mass m, which moves positive to the right. When stationary in the position shown, all springs are undeflected. Using BOBODDY, find the mathematical model of this system assuming small rotation angle 0. Link, moment of inertia J k3 L₁ 12 5 Ꮎ wwww Figure 3: Mechanical System m k₂ b
A solid is bounded below by the cone z=√x +y and above by the plane z = 1. Find the center of mass and the moment of inertia about the z-axis if the density is 8(r,0,z) = 5z. The center of mass is (x,y,z) = ( (Type an integer or a simplified fraction.)

SEE MORE QUESTIONS

Recommended textbooks for you

International Edition---engineering Mechanics: St…

Mechanical Engineering

ISBN:

9781305501607

Author:

Andrew Pytel And Jaan Kiusalaas

Publisher:

CENGAGE L