Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977237
Author: BEER
Publisher: MCG
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Chapter B, Problem B.10P
To determine
The mass moment of inertia of the solid about the x axis.
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Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point
O.
-0.80h
Answers:
lx = i
ly= i
lo = i
0.67h
-0.80h
h4
h4
h4
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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- The moment of inertia of the plane region about the x-axis and the centroidal x-axis are Ix=0.35ft4 and Ix=0.08in.4, respectively. Determine the coordinate y of the centroid and the moment of inertia of the region about the u-axis.arrow_forwardThe moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4, respectively. Determine y (the y-coordinate of the centroid C) and Ix (the moment of inertia about the centroidal x-axis).arrow_forwardDetermine the product of inertia with respect to the x- and y-axes for the quarter circular, thin ring (tR) by integration.arrow_forward
- The slender bar lies in the x-y plane. Its mass is 6 kg and the material is homogeneous. Use integration to determine its moment of inertia about the z-axisarrow_forwardFor the same case, consider the moment of inertia about each of the four axes. About which axis will the MoI be the smallest number?arrow_forwarddetermine the moment of inertia of the quarter of the circle having a radius of 6 m. a with respect to the given axis b with respect to a centroidal axis c determine the polar moment of inertia relative to the polar axis through one of its cornerarrow_forward
- Show the complete solution.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_forwardThe variable h designates the arbitrary vertical location of the center of the circular cutout within the semicircular area. Determine the area moment of inertia about the x-axis for (a) h = 0 and (b) h = 6 in. 4" 16" h Amswers: (a) h = 0 in.4 (b) h = 6 in. Ix= in.4arrow_forward
- Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis. Take h = 1.3 in. (Round the moment of inertia to one decimal place and the radius of gyration to three decimal places.)arrow_forwardDetermine the moments of inertia of the triangular area about its base and about parallel axes through its centroid and vertex.arrow_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_forward
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