Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
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Chapter B, Problem B.20P
To determine
The mass moment of inertia of hemispherical shell and radius of gyration about x-axis.
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Knowing that the thin hemispherical shell shown has a mass m and thickness t , determine the mass moment of inertia and the radius of gyration of the shell with respect to the x axis)Hint: Consider the shell as formed by removing a hemisphere of radius r from a hemisphere of radius r +t ; then neglect the terms containing t2 and t3 and keep those terms containing t.)
The quarter ring shown has a mass m and was cut from a thin, uniform plate. Knowing that ri = 3/4 r^2, determine the mass moment of inertia of the quarter ring with respect to (a) the axis AA', (b) the centroidal axis CC' that is perpendicular to the plane of the quarter ring. Please include a sketch of the problem.
Determine by direct integration the mass moment of inertia with respect to the z axis of the right circular cylinder shown, assuming that it has a uniform density and a mass m.
Chapter B Solutions
Vector Mechanics For Engineers
Ch. B - A thin plate with a mass m is cut in the shape of...Ch. B - Prob. B.2PCh. B - Prob. B.3PCh. B - Prob. B.4PCh. B - A piece of thin, uniform sheet metal is cut to...Ch. B - Prob. B.6PCh. B - Prob. B.7PCh. B - Prob. B.8PCh. B - Prob. B.9PCh. B - Prob. B.10P
Ch. B - Prob. B.11PCh. B - Prob. B.12PCh. B - Determine by direct integration the mass moment of...Ch. B - Prob. B.14PCh. B - A thin, rectangular plate with a mass m is welded...Ch. B - A thin steel wire is bent into the shape shown....Ch. B - Prob. B.17PCh. B - Prob. B.18PCh. B - Prob. B.19PCh. B - Prob. B.20PCh. B - Prob. B.21PCh. B - Prob. B.22PCh. B - Prob. B.23PCh. B - Prob. B.24PCh. B - Prob. B.25PCh. B - Prob. B.26PCh. B - Prob. B.27PCh. B - Prob. B.28PCh. B - Prob. B.29PCh. B - Prob. B.30PCh. B - Prob. B.31PCh. B - Determine the mass moments of inertia and the...Ch. B - Prob. B.33PCh. B - Prob. B.34PCh. B - Prob. B.35PCh. B - Prob. B.36PCh. B - Prob. B.37PCh. B - Prob. B.38PCh. B - Prob. B.39PCh. B - Prob. B.40PCh. B - Prob. B.41PCh. B - Prob. B.42PCh. B - Prob. B.43PCh. B - Prob. B.44PCh. B - A section of sheet steel 2 mm thick is cut and...Ch. B - Prob. B.46PCh. B - Prob. B.47PCh. B - Prob. B.48PCh. B - Prob. B.49PCh. B - Prob. B.50PCh. B - Prob. B.51PCh. B - Prob. B.52PCh. B - Prob. B.53PCh. B - Prob. B.54PCh. B - Prob. B.55PCh. B - Determine the mass moment ofinertia of the steel...Ch. B - Prob. B.57PCh. B - Prob. B.58PCh. B - Determine the mass moment of inertia of the...Ch. B - Prob. B.60PCh. B - Prob. B.61PCh. B - Prob. B.62PCh. B - Prob. B.63PCh. B - Prob. B.64PCh. B - Prob. B.65PCh. B - Prob. B.66PCh. B - Prob. B.67PCh. B - Prob. B.68PCh. B - Prob. B.69PCh. B - Prob. B.70PCh. B - For the component described in the problem...Ch. B - Prob. B.72PCh. B - For the component described in the problem...Ch. B - Prob. B.74P
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- A thin plate with a mass m has the trapezoidal shape shown. Determine the mass moment of inertia of the plate with respect to (a) the centroidal axis CC’ that is perpendicular to the plate, (b) the axis AA’ that is parallel to the x axis and is located at a distance 1.5a from the plate.arrow_forwardDetermine the mass moment of inertia of a ring of mass m, cut from a thin uniform plate, with respect to (a) the axis AA', (b) the centroidal axis CC' that is perpendicular to the plane of the ring.arrow_forwardA square hole is centered in and extends through the aluminum machine component shown. Determine (a) the value of a for which the mass moment of inertia of the component is maximum with respect to the axis AA’ that bisects the top surface of the hole, (b) the corresponding values of the mass moment of inertia and the radius of gyration with respect to the axis AA’. (The specific weight of aluminum is 0.100 lb/in3).arrow_forward
- A thin plate with a mass m is cut in the shape of an equilateral triangle of side a . Determine the mass moment of inertia of the plate with respect to (a) the centroidal axes AA' and BB',(b) the centroidal axis CC ’ that is perpendicular to the plate.arrow_forwardA thin, semielliptical plate has a mass m . Determine the mass moment of inertia of the plate with respect to (a) the centroidal axis BB, (b) the centroidal axis CC ’ that is perpendicular to the plate.arrow_forwardA thin plate with a mass m has the trapezoidal shape shown. Determine the mass moment of inertia of the plate with respect to (a) the x axis, (b) the y axis.arrow_forward
- The thin plate shown is composed of a square plate of mass 80 kg and a quarter-circular plate of mass 50 kg. What is the mass moment of inertia of the shape about the y-axis?arrow_forwardA subassembly for a model airplane is fabricated from three pieces of 1.5-mm plywood. Neglecting the mass of the adhesive used to assemble the three pieces, determine the mass moment of inertia of the subassembly with respect to each of the coordinate axes. (The density of the plywood is 780 kg/m3.)arrow_forwardThe homogeneous circular cone shown has a mass m . Determine the mass moment of inertia of the cone with respect to the line joining the origin O and pont A.arrow_forward
- 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.arrow_forwarddetermine the mass moment of inertia of steel balls used in ball bearings. Use a diameter of 2cmarrow_forwardGiven an arbitrary body and three rectangular axes x, y, and z,, prove that the mass moment of inertia of the body with respect to any one of the three axes cannot be larger than the sum of the mass moments of inertia of the body with respect to the other two axes. That is, prove that the inequality Ix ≤ Iy +Iz and the two similar inequalities are satisfied. Furthermore, prove that Iy _> 1/2Ix if the body is a homogeneous solid of revolution, where x is the axis of revolution and y is a transverse axis.arrow_forward
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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY