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.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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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.
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 shaded area has the following properties:
4 = 126 x10 mm* ; 1, = 6,55 x10* mm* ; and
Pay =-1.02 10° mm*
Determine the moments of inertia of the area about
the x' and v' axes if e=30°.
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 homogeneous wire with a mass per unit length of 0.056 kg/m is used to form the figure shown. Determine the mass moment of inertia of the wire with respect to each of the coordinate axes.arrow_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_forwardDetermine 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_forward
- A 0.2m hole is drilled into a 0.6m x 0.6m x 0 2m plate. The plate weighs 98 kN/m3. Determine the moment of Inertia about x, y, and z axis.arrow_forwardDetermine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/meter cubearrow_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_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_forwardDetermine the moment of inertia about the y-axis of the shaded area of the figure shown:*arrow_forwardThe pendulum consists of a slender rod with a mass 1.6 kg and a circular plate with a mass of 4.7 kg. h= 2.7 m and d= 1.7m. h Find the Mass Moment of Inertia about the point O in kg*m². Give your answer with one decimal.arrow_forward
- Show using analytical methods how the mass moment of inertia changes for a uniform rod by changing the axis about which it rotates. Z Figure 1 - Uniform Rod Q1 dr Larrow_forwardThe 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_forward4) Please determine the mass moment of inertia of the steel body that shown in the figure with respect to the Y (vertical) axis. Dimensions are in millimeters. Density of the steel body is 7800 kg/m³. (L = 100) R20 Y axis 30arrow_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