VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
12th Edition
ISBN: 9781260265521
Author: BEER
Publisher: MCG
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Chapter B, Problem B.21P
To determine
(a)
The value of
To determine
(b)
The value of MI about
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A 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).
A thin plate with a mass m was cut in the shape of a parallelogram as shown. Determine the mass moment of inertia of the plate with respect to (a) the x axis, (b) the axis BB’ that is perpendicular to the plate.
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Chapter B Solutions
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
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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- find the polar moment of inertia of thin triangular plate a bounded by the line y = x, y=-x and y = 1 if &(x,y) = y + 1 kg m2arrow_forward100 mm Problem (3) A 3-mm thick piece of aluminum sheet metal is cut and bent into the machine component shown. The density of aluminum is 2770 kg/m³. Determine the mass moment of inertia of the component with respect to the y-axis. 180 mm 160 mm 240 mm 160 mmarrow_forwardFor items 4 and 5. A thin rectangular plate is welded on the center of the top of a circular cylinder. The mass of the cylinder is 5kg and the mass of the triangular plate is 2kg. Note that the x-axis is located on the centroidal x-axis of the triangular plate. 30cm 26cm 0.1725 m diam. d=7cm X 10cm 4. Which of the following is closest to the moment of inertia of the composite object about the x- axis? 0.208 kg-m^2 5. Which of the following is closest to the radius of gyration of the composite object about the x- axis?arrow_forward
- inertia of the assembly with respect to (a) the x axis, (b) the y axis, (c) the z axis. (The density of steel is 7850 kg/m³.) The machine element shown is fabricated from steel. Determine the mass moment of 40 mm 40 mm 20 mm 20 mm 80 mm 60 mm 40 mmarrow_forwardA thin uniform rod of mass M and length L is bent at its center so that the two segments are now perpendicular to each other. Find its moment of inertia about an axis perpendicular to its plane and passing through (a) the point where the two segments meet and (b) the midpoint of the line connecting its two ends.arrow_forwardA section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the component.arrow_forward
- A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass moment of inertia of the component with respect to each of the coordinate axes.arrow_forwardA section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the component.arrow_forwardA piece of thin, uniform sheet metal is cut to form the machine component shown. Denoting the mass of the component by m , determine its mass moment of inertia with respect to (a) the axis AA,(b) the axis BB ’, where the AA and BB ’ axes are parallel to the x axis and lie in a plane parallel to and at a distance a above the xz plane.arrow_forward
- A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the component.arrow_forwardShown is the cross section of an idler roller. Determine its mass moment of inertia and its radius of gyration with respect to the axis AA ’. (The specific weight of bronze is 0.310 lb/in3 ; of aluminum, 0.100 lb/in3 ; and of neoprene, 0.0452 lb/in3).arrow_forwardFor the shape shown, determine (a) the polar moment of inertia of the circular area alone (without the square hole), (b) the polar moment of inertia of the area shown (with the square hole), (c) the percent change in moment of inertia in the shape by having added the square hole, (d) the percent change in area by having added the square hole. (The square is centered on the circle.) rarrow_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