PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 21, Problem 17P
The bent rod has a weight of 1.5 lb/ft. Locate the center of gravity G(
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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 = 7.9 kg and b = 485 mm.
Answers:
1xxx =
i
lyy= i
Izz =
i
kg.m²
kg-m²
kg-m²
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
Determine the moment of Inertia Ix (mm4) about the x-axis.
Given:
X1 = 1.6 mm
x2 = 8 mm
Y₁ = 1.8 mm
Y2 = 9 mm
X₂
X₁
У1
Y₂
X
Chapter 21 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 21 - Show that the sum of the moments of inertia of a...Ch. 21 - Prob. 2PCh. 21 - Prob. 3PCh. 21 - Determine the moments of inertia Ix and Iy of the...Ch. 21 - Prob. 5PCh. 21 - Determine by direct integration the product of...Ch. 21 - Prob. 9PCh. 21 - Prob. 10PCh. 21 - Determine the moment of inertia Ixx of the...Ch. 21 - Prob. 13P
Ch. 21 - Prob. 14PCh. 21 - Prob. 15PCh. 21 - The bent rod has a weight of 1.5 lb/ft. Locate the...Ch. 21 - If a body contains no planes of symmetry, the...Ch. 21 - Prob. 23PCh. 21 - Prob. 25PCh. 21 - Prob. 28PCh. 21 - Prob. 29PCh. 21 - Prob. 30PCh. 21 - The 2-kg thin disk is connected to the slender rod...Ch. 21 - Prob. 33PCh. 21 - Prob. 36PCh. 21 - Prob. 37PCh. 21 - Prob. 40PCh. 21 - Prob. 41PCh. 21 - Prob. 42PCh. 21 - Prob. 48PCh. 21 - Prob. 51PCh. 21 - Prob. 54PCh. 21 - Show that the angular velocity of a body, in terms...Ch. 21 - A thin rod is initially coincident with the Z axis...Ch. 21 - The top consists of a thin disk that has a weight...Ch. 21 - Prob. 66PCh. 21 - Prob. 69PCh. 21 - Prob. 70PCh. 21 - Prob. 73PCh. 21 - Prob. 74PCh. 21 - Prob. 77P
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- The molded plastic block has a density of 1300 kg/m³. Calculate its moment of inertia about the y-y axis. What percentage error e is introduced by using the approximate relation 1/3 ml² for lxx? Answers: lyy e = = 200 y 495 200 Dimensions in millimeters textes kg m² % 60 60arrow_forwardFind 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 ✔arrow_forwardA 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_forward
- The hammer consists of a cast iron head and wood handle. The iron head has 7000 kg/m3 density, and its shape is a rectangular prism with a circular hole. The wood handle has 500 kg/m3 density, and its shape is a circular cylinder. Determine the mass moment of inertia about the z axis and the corresponding radius of gyration. 30 mm 30 mm 80 mm 20 mm х Z. 40 mm 40 mmarrow_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 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 = 4 in. y 3" 12" h LL Amswers: (a) h = 0 in.4 (b) h = 4 in. Ix= i in.4arrow_forward
- The molded plastic block has a density of 1300 kg/m³. Calculate its moment of inertia about the y-y axis. What percentage error e is introduced by using the approximate relation 1/3 ml² for lxx? Answers: lyy= e= i i -185 y 445 185 Dimensions in millimeters 740 140 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 = 5 in. 3" 11" h Amswers: (a) h = 0 Ix = i in.4 (b) h = 5 in. Ix= i in.4arrow_forwardA) Determine the position of the center of gravity of the figure's structure. B)Determine the moment of inertia of mass with respect to the x' axis that passes through the structure's center of gravity and is parallel to the x axis. The cone has a density of 600 kg/m3 and the cylinder a density of 800 kg/m3. Consider H = 83arrow_forward
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