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.39P
To determine
The mass product of the inertia
The mass product of the inertia
The mass product of the inertia
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The machine element shown is fabricated from steel, where h = 64 mm. The density of Steel is
y
40 mm
20 mm-
80 mm
40 mm
20 mm
40 mm
Determine the mass moment of inertia of the assembly with respect to the z axis.
The mass moment of inertia of the assembly with respect to the z axis is
x
10-3 kg-m².
A rod of mass 0.9 kg/m is welded to a
hollow disc of mass 3 kg/m² as shown.
Determine the mass moment of inertia
about the axes y and z, Iyy and Izz.
0.15:
R 0.05 m
0.1 m
0.3 m
0.1 m
X
The machine element shown is fabricated from steel. Determine the mass moment of 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.)
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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- 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_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_forwardh Determine the moment of inertia and radius of gyration of the composite shape with respect to the x- and y-axes knowing that b=4 cm, h = 5 cm, T₁ = 2 cm, and r₁ = 1.333 cm. For the x-axis L₂ = b For the y axis I₂ = k₂ = ky =arrow_forward
- Determine the moments of inertia about the centroidal x-axes of the trapezoidal area. a=147 mm; b=294 mm; h=441 mm. Answer the question in mm4. Yanıt: b b Yanıt: Answer the question in mm4. h Determine the moments of inertia about the centroidal y-axes of the trapezoidal area. X Warrow_forwardThe figure shown is formed of 1.5-mm-diameter aluminum wire. Knowing that the density of aluminum is 2800 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure.arrow_forwardDetermine the moments of inertia I, I, and Jo in ft* for the section. X' y' y 11 ft 5.5 ft 22 ft ft4 Ix ft4 %D ft4 Finally, determine the radii of gyration ky, ky and ko in feet. ft ky ft Ky Ко ft II IIarrow_forward
- The mass moment of inertia of a thin ring of mass m and radius R about the z axis is A. (1/4) mR2 B. (1/2) mR2 C. 2 mR2 D. MR2arrow_forwardFor the section shown, a. Determine the moment of inertia with respect to the X-axis b. Determine the moment of inertia with respect to the Y-axis c. Determine the moment of inertia with respect to the X'-axis 40 mm X' 30° t, = 40 mm %3D 40 mm 200 mm ww 008arrow_forwardfind 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_forward
- By the method of this article, determine the moments of inertia about the x-and y-axes of the trapezoidal area. 1.5b 1.5b 1.3b b Answers: Ix= i ba baarrow_forwardThe moment of inertia with respect to the x and y axis have been computed and are known to be I = 1.66 x 104 mm'and I, = 1.12x 10 mm, Determine the orientation of the principal axes of the section about O, and the values of the principal moments on inertia of the section about O. G0mm 10mm 80mm 10mm 10mm 60mmarrow_forwardDetermine the mass moment of inertia of the steel machine element shown with respect to the y axis. (The specific weight of steel is 490 lb/ft3.)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