Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 21.1, Problem 13P
To determine
The product of inertia
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Given the thin square plate:
Determine mass moment of inertia:
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
%
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
60
Chapter 21 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 21.1 - Show that the sum of the moments of inertia of a...Ch. 21.1 - Prob. 2PCh. 21.1 - Prob. 3PCh. 21.1 - Determine the moments of inertia Ix and Iy of the...Ch. 21.1 - Prob. 5PCh. 21.1 - Determine by direct integration the product of...Ch. 21.1 - Prob. 7PCh. 21.1 - Prob. 8PCh. 21.1 - Prob. 9PCh. 21.1 - Prob. 10P
Ch. 21.1 - Prob. 11PCh. 21.1 - Determine the moment of inertia Ixx of the...Ch. 21.1 - Prob. 13PCh. 21.1 - Prob. 14PCh. 21.1 - Prob. 15PCh. 21.1 - Prob. 16PCh. 21.1 - The bent rod has a weight of 1.5 lb/ft. Locate the...Ch. 21.1 - Prob. 18PCh. 21.1 - Prob. 19PCh. 21.1 - Prob. 20PCh. 21.1 - Prob. 21PCh. 21.3 - If a body contains no planes of symmetry, the...Ch. 21.3 - Prob. 23PCh. 21.3 - The 15-kg circular disk spins about its axle with...Ch. 21.3 - Prob. 25PCh. 21.3 - Prob. 26PCh. 21.3 - Prob. 27PCh. 21.3 - Prob. 28PCh. 21.3 - Prob. 29PCh. 21.3 - Prob. 30PCh. 21.3 - Prob. 31PCh. 21.3 - The 2-kg thin disk is connected to the slender rod...Ch. 21.3 - Prob. 33PCh. 21.3 - Prob. 34PCh. 21.3 - The 200-kg satellite has its center of mass at...Ch. 21.3 - Prob. 36PCh. 21.3 - Prob. 37PCh. 21.3 - Determine the kinetic energy of the 7-kg disk and...Ch. 21.3 - Prob. 39PCh. 21.3 - Prob. 40PCh. 21.4 - Prob. 41PCh. 21.4 - Prob. 42PCh. 21.4 - Prob. 43PCh. 21.4 - Prob. 44PCh. 21.4 - Prob. 45PCh. 21.4 - The assembly is supported by journal bearings at A...Ch. 21.4 - Prob. 47PCh. 21.4 - Prob. 48PCh. 21.4 - Prob. 49PCh. 21.4 - Prob. 50PCh. 21.4 - Prob. 51PCh. 21.4 - Prob. 52PCh. 21.4 - Prob. 53PCh. 21.4 - Prob. 54PCh. 21.4 - Prob. 55PCh. 21.4 - Prob. 56PCh. 21.4 - The blades of a wind turbine spin about the shaft...Ch. 21.4 - Prob. 58PCh. 21.4 - The thin rod has a mass of 0.8 kg and a total...Ch. 21.4 - Show that the angular velocity of a body, in terms...Ch. 21.4 - A thin rod is initially coincident with the Z axis...Ch. 21.6 - The gyroscope consists of a uniform 450-g disk D...Ch. 21.6 - The toy gyroscope consists of a rotor R which is...Ch. 21.6 - The top consists of a thin disk that has a weight...Ch. 21.6 - Solve Prob. 2164 when =90.Ch. 21.6 - Prob. 66PCh. 21.6 - Prob. 67PCh. 21.6 - Prob. 68PCh. 21.6 - Prob. 69PCh. 21.6 - Prob. 70PCh. 21.6 - Prob. 71PCh. 21.6 - Prob. 72PCh. 21.6 - Prob. 73PCh. 21.6 - Prob. 74PCh. 21.6 - Prob. 75PCh. 21.6 - Prob. 76PCh. 21.6 - Prob. 77PCh. 21.6 - Prob. 78P
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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 Ixx? Answers: lyy= 0.8 185 1.108 y 445 185 Dimensions in millimeters 140 140 % kg.m²arrow_forwardThis question is specifically a Statics problem. Determine the moment of inertia of the shape with respect to the horizontal axis passing through its centroid.arrow_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 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_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_forward0.4m-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_forward
- 1. Determine the moment of inertia about an axis perpendicular to the page and passing through the pin at 0. The thin plate has a hole in its center. Its thickness is 50 mm, and the material has a density of p = 60 kg/m³. What is the radius of gyration about this point? 150 mm 1.40 m 1.40 marrow_forwardThe pendulum consists of the 3-kg slender rod and the 5-kg thin plate. Determine the location ỹ of the center of mass G of the pendulum; then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G. y 2 m G 0.5 m Eim-arrow_forwardDetermine the moment of inertia about an axis perpendicular to the screen and passing through the center of mass G of the assembly. The block has a mass of 3.5 kg and the semicylinder has a mass of 8.5 kg. y 400 mm G 200 mm 300 mmarrow_forward
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