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.50P
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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In the figure the L- shaped machine part is composed of two homogeneous bars . Bar 1 is tungsten alloy with mass density 14,000 kg/m3 , and bar 2 is steel with mass density 7800 kg/m3 . Determine its moment of inertia about the x axis.
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.
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O A. SS F(x,y) dy dx
O B.
OB. F(x,y) dx dy
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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
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Q
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Show using analytical methods how the mass moment of inertia changes for a
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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 moment of inertia about the y-axis of the shaded area of the figure shown:*arrow_forwardA 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_forwardThe 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.arrow_forward
- Determine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/meter cubearrow_forwardY YI R a a image 1 barrow_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
- Determine 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_forwardCalculate the Moment of Inertia of the given lamina, for the dimensions B=20mm, D=30mm, b=15mm and d=25mm. y A B E C.G X - X d D H D b Barrow_forwardA lamina with constant density p(x, y) = p occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The rectangle 0 s xS 4b, 0 sys 4h. Iỵ = Iy y = Ilxarrow_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_forwardCalculate 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 mass moment of inertia and radius of gyration of the figure shown about the x, y and z axis. The materials weighs 30kN/m³. 0.60m 0.9m 0.30m 0.10 '0.05m 0.50m 0.45m 0.10m 0.20 0.20 0.20arrow_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