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

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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

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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
Equation of Motion The triangle is made of 3 rods of a length 1-2.1ft and density is p = 4 lb/ft. ^ 1) Establish what you think is the best Coordinate system for this problem and explain why. 2) Find the location of the center of gravity (x bar and y bar). 3) Find the weight of the triangle. 4) Find the Mass Moment of Inertia at O of the triangle. 5) Draw the FBD and kinetic diagram of the triangle. 6) Find the accelerations of the triangle (angular and linear). 7) Find the Pin Reaction at O: . On and Ot • or Ox and Oy . • Magnitude O, and direction. In the box below, enter the angular acceleration & in rad/s with one decimal. Include the sign + if CCW or - sign if CW.
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The inertia matrix about O, 1(0, x, y, z), of a cylinder of height H, radius Rand mass M is: R M 2 M R²/2 + H²/6 0 0 R² 0 0 R²/2+ H2/6, 0 *(****) R² 0 R²/2+2H²/3/ 2 R²/2+2H²/3 0 0 0 0 0 0 0 R²/2 + H²/6 0 * (****) R²/2 + H²/6 0 0 0 0 R² H
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?
Please help me by solving it on paper. I don't want matlab script. Plz
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Many rotating mechanical components can be modeled as a disk with a hole as shown below. Examples include pulleys, gears, bearings, rollers, sprockets, tires, and wheels. Determine the general solution for mass moment of inertia of a disk with a hole as a function of mass (m), outer diameter (D), inner diameter (d), and width (w). Although your solution must not include density, it may be helpful to find density as an intermediate equation. D m:mass
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