PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 21, Problem 13P
To determine
The product of inertia
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This question is specifically a Statics problem.
Determine the moment of inertia of the shape with respect to the horizontal axis passing through its centroid.
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
%
Determine the moment of inertia of the homogenous triangular prism with respect to the y axis. Express the result in terms of the mass m of the prism. Hint: For integration, use thin plate elements parallel to the x–y plane having a thickness of dz.
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_forwardDetermine 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 6000 kg/m3 and the cylinder a density of 8000 kg/m3. Consider H = 83arrow_forwardDetermine the moment of inertia of the solid steel assembly about the x axis. Steel has a specific weight of Ya - 490 lb/ft³. 0.25 ft 0.5 ft -3 ftarrow_forward
- Determine the moment of inertia of the solid steel assembly about the x-axis. The specific weight of steel is Yst = 488 lb/ft3. 0.25 pie -2 pies- 3 pies ļ 0.5 pie Xarrow_forwardThe 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 Ixx? Answers: lyy= 0.8 185 1.108 y 445 185 Dimensions in millimeters 140 140 % kg.m²arrow_forwardDetermine the product of inertia of the thin strip of area with respect to the x and y axes. The strip is oriented at an angle from the axis. Assume that t << I. Express your answer in terms of the variables 1, t, and 0.arrow_forward
- Specifically a Statics problem. Determine the moment of inertia of the shape with respect to the horizontal axis passing through its centroid (all dimensions in mm).arrow_forwardGiven the thin square plate: Determine mass moment of inertia:arrow_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
- 0.4m-0.4 m- 1.5 m 0.1 m %23 03m The pendulum consists of two slender rods AB and OC which have a mass per unit length of 3.00 kg m The thin plate has a mass of 12 kg m Determine the moment of inertia of the pendulum about an axis perpendicular to the page and passing through the pin at 0arrow_forwardThe S-shaped piece is formed from a rod of diameter d and bent into the two semicircular shapes. Determine the products of inertia for the rod, for which d is small compared with r. The total mass of the piece is m = 9.1 kg and the distance r is 395 mm. Answers: Ixy = Ixz = lyz = i i i d kg-m² kg-m² kg-m²arrow_forwardDetermine the moment of inertia of the profile below in relation to the x axis. Make the entire calculation of the question.arrow_forward
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