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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Question
Chapter B, Problem B.70P
To determine
(a)
The principal mass moment of inertias at the origin.
To determine
(a)
The principal axis about the origin.
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Determine the products of inertia about the coordi-
nate axes for the thin plate of mass m which has
the shape of a circular sector of radius a and angle
ß as shown.
Z
|
В
a
m
8
The homogeneous plate of Prob. B/7 is repeated
here. Determine the product of inertia for the plate
about the x-y axes. The plate has mass m and uni-
form thickness t.
x = ky²
B/7 For the thin homogeneous plate of uniform thickness
t and mass m, determine the mass moments of inertia
about the x'-, y'-, and z'-axes through the end of the
plate at A. Refer to the results of Sample Problem B/4
and Table D/3 in Appendix D as needed.
x = ky²
Thickness t
Problem B/7
The uniform rod of length 4b and mass m is
bent into the shape shown. The diameter of
the rod is small compared with its length.
Determine the moments of inertia of the rod
about the three coordinate axes. Use the
values m = 9.7 kg and b = 650 mm.
Answers:
Ixx = i
lyy=
Izz
i
i
kg-m²
kg.m²
kg.m²
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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- 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_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_forwardThe 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_forward
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- By the method of this article, determine the moments of inertia about the x- and y-axes of the trapezoidal area. 1.7b 1.7b 0.9b Answers: Ix = i b4 i b4arrow_forwardDetermine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/meter cubearrow_forwardDetermine the moment of inertia about the AB axis. Fig (3)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