Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977237
Author: BEER
Publisher: MCG
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Chapter B, Problem B.48P
To determine
The product of mass moment of inertia
The product of mass moment of inertia
The product of mass moment of inertia
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Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = 7y - 3y² and the line x + 2y = 0 if 8(x,y) = x + 2y.
Choose the correct sketch of the plate described above.
O A.
Q
O A. SS F(x,y) dy dx
O B.
OB. F(x,y) dx dy
Q
Select the order of integration that will make the computations easier and fill in the limits of integration in your choice.
G
O C.
O D.
Use the given density function 8 to write the appropriate integrand F(x,y) for finding the moment of inertia. Then substitute into the correct integral from the previous step and evaluate to find the moment of inertia for the plate.
The moment of inertia is
(Simplify your answer.)
Q
Q
✔
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
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Calculate the Moment of
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the dimensions B=20mm,
D=30mm, b=15mm and
d=25mm.
y
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E
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X -
X d D
H
D
b
B
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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- Determine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/m³. 0.10m AY 0.30m 0.10m 0.60m 0.05m 0.20m Z. 0.10 0.40marrow_forward3. If the large ring, small ring, and each spoke weigh 90 lb, 20 lb, and 15 lb respectively. Find the mass moment of inertia of an axis that extends perpendicular to the page and passes through point A. ✔ S.W. O 1 ft- 4 ftarrow_forwardDetermine 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_forward
- Calculate moment of inertia of the shape shown with respect to the x axis where a=0.8 in, b= 1.5 in. and r= 1.2 in. lx= in4 2 b Xarrow_forwardFind the moment of inertia about centroidal X-axis and centroidal Y-axis of the given geometry .arrow_forwardDetermine the mass moment of inertia of the figure shown about the x, y and z axis. The materials weighs 500N/m3. Also determine the radius of gyration about each axis.arrow_forward
- 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.m²arrow_forwardFormulas Moments of Inertia x= [y²d ly = fx²dA Theorem of Parallel Axis Ixr = 1 + d² A * axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between x and x' ly₁ = 15+d²A ỹ axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1=Σ 4 All the moments of inertia should be about the same axis. Radius of Gyration k=arrow_forwardDetermine the moment of inertia and the radius of gyration of the shaded area shown with respect to the x 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