VECTOR MECHANIC
12th Edition
ISBN: 9781264095032
Author: BEER
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 9.5, Problem 9.121P
The area shown is revolved about the x axis to form a homogeneous solid of revolution of mass m. Determine by direct integration the mass moment of inertia of the solid with respect to the x axis. Express your answers in terms of m, a, and n.
Fig. P9.121
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The area shown is revolved about the x axis to form a homogeneous solid of revolution of mass m . Determine by direct integration the mass moment of inertia of the solid with respect to (a) the x axis, (b) the y axis. Express your answers in terms of m and the dimensions of the solid.
100 mm
Problem (3) A 3-mm thick piece of aluminum sheet metal is
cut and bent into the machine component shown. The density
of aluminum is 2770 kg/m³. Determine the mass moment of
inertia of the component with respect to the y-axis.
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160 mm
240 mm
160 mm
Chapter 9 Solutions
VECTOR MECHANIC
Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.8PCh. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...
Ch. 9.1 - Prob. 9.11PCh. 9.1 - Prob. 9.12PCh. 9.1 - 9.12 through 9.14 Determine by direct integration...Ch. 9.1 - 9.12 through 9.14 Determine by direct integration...Ch. 9.1 - Prob. 9.15PCh. 9.1 - Prob. 9.16PCh. 9.1 - Prob. 9.17PCh. 9.1 - Prob. 9.18PCh. 9.1 - Determine the moment of inertia and the radius of...Ch. 9.1 - Prob. 9.20PCh. 9.1 - Determine the polar moment of inertia and the...Ch. 9.1 - Prob. 9.22PCh. 9.1 - Prob. 9.23PCh. 9.1 - 9.23 and 9.24 Determine the polar moment of...Ch. 9.1 - Prob. 9.25PCh. 9.1 - Prob. 9.26PCh. 9.1 - Prob. 9.27PCh. 9.1 - Prob. 9.28PCh. 9.1 - Prob. 9.29PCh. 9.1 - Prove that the centroidal polar moment of inertia...Ch. 9.2 - 9.31 and 9.32 Determine the moment of inertia and...Ch. 9.2 - 9.31 and 9.32 Determine the moment of inertia and...Ch. 9.2 - 9.33 and 9.34 Determine the moment of inertia and...Ch. 9.2 - 9.33 and 9.34 Determine the moment of inertia and...Ch. 9.2 - Determine the moments of inertia of the shaded...Ch. 9.2 - Determine the moments of inertia of the shaded...Ch. 9.2 - Prob. 9.37PCh. 9.2 - Prob. 9.38PCh. 9.2 - Prob. 9.39PCh. 9.2 - Prob. 9.40PCh. 9.2 - 9.41 through 9.44 Determine the moments of inertia...Ch. 9.2 - 9.41 through 9.44 Determine the moments of inertia...Ch. 9.2 - Prob. 9.43PCh. 9.2 - Prob. 9.44PCh. 9.2 - 9.45 and 9.46 Determine the polar moment of...Ch. 9.2 - Prob. 9.46PCh. 9.2 - 9.47 and 9.48 Determine the polar moment of...Ch. 9.2 - 9.47 and 9.48 Determine the polar moment of...Ch. 9.2 - To form a reinforced box section, two rolled W...Ch. 9.2 - Two channels are welded to a d 12-in. steel plate...Ch. 9.2 - Prob. 9.51PCh. 9.2 - Two 20-mm steel plates are welded to a rolled S...Ch. 9.2 - A channel and a plate are welded together as shown...Ch. 9.2 - Prob. 9.54PCh. 9.2 - Two L76 76 6.4-mm angles are welded to a C250 ...Ch. 9.2 - Prob. 9.56PCh. 9.2 - Prob. 9.57PCh. 9.2 - 9.57 and 9.58 The panel shown forms the end of a...Ch. 9.2 - Prob. 9.59PCh. 9.2 - Prob. 9.60PCh. 9.2 - Prob. 9.61PCh. 9.2 - Prob. 9.62PCh. 9.2 - Prob. 9.63PCh. 9.2 - Prob. 9.64PCh. 9.2 - Prob. 9.65PCh. 9.2 - Prob. 9.66PCh. 9.3 - 9.67 through 9.70 Determine by direct integration...Ch. 9.3 - 9.67 through 9.70 Determine by direct integration...Ch. 9.3 - 9.67 through 9.70 Determine by direct integration...Ch. 9.3 - Prob. 9.70PCh. 9.3 - Prob. 9.71PCh. 9.3 - Prob. 9.72PCh. 9.3 - Prob. 9.73PCh. 9.3 - 9.71 through 9.74 Using the parallel-axis theorem,...Ch. 9.3 - Prob. 9.75PCh. 9.3 - 9.75 through 9.78 Using the parallel-axis theorem,...Ch. 9.3 - Prob. 9.77PCh. 9.3 - Prob. 9.78PCh. 9.3 - Determine for the quarter ellipse of Prob. 9.67...Ch. 9.3 - Determine the moments of inertia and the product...Ch. 9.3 - Determine the moments of inertia and the product...Ch. 9.3 - 9.75 through 9.78 Using the parallel-axis theorem,...Ch. 9.3 - Determine the moments of inertia and the product...Ch. 9.3 - Determine the moments of inertia and the product...Ch. 9.3 - Prob. 9.85PCh. 9.3 - 9.86 through 9.88 For the area indicated,...Ch. 9.3 - Prob. 9.87PCh. 9.3 - Prob. 9.88PCh. 9.3 - Prob. 9.89PCh. 9.3 - 9.89 and 9.90 For the angle cross section...Ch. 9.4 - Using Mohrs circle, determine for the quarter...Ch. 9.4 - Using Mohrs circle, determine the moments of...Ch. 9.4 - Prob. 9.93PCh. 9.4 - Using Mohrs circle, determine the moments of...Ch. 9.4 - Using Mohrs circle, determine the moments of...Ch. 9.4 - Using Mohrs circle, determine the moments of...Ch. 9.4 - For the quarter ellipse of Prob. 9.67, use Mohrs...Ch. 9.4 - 9.98 though 9.102 Using Mohrs circle, determine...Ch. 9.4 - Prob. 9.99PCh. 9.4 - 9.98 though 9.102 Using Mohrs circle, determine...Ch. 9.4 - Prob. 9.101PCh. 9.4 - Prob. 9.102PCh. 9.4 - Prob. 9.103PCh. 9.4 - 9.104 and 9.105 Using Mohrs circle, determine the...Ch. 9.4 - 9.104 and 9.105 Using Mohrs circle, determine the...Ch. 9.4 - For a given area, the moments of inertia with...Ch. 9.4 - it is known that for a given area Iy = 48 106 mm4...Ch. 9.4 - Prob. 9.108PCh. 9.4 - Prob. 9.109PCh. 9.4 - Prob. 9.110PCh. 9.5 - A thin plate with a mass m is cut in the shape of...Ch. 9.5 - A ring with a mass m is cut from a thin uniform...Ch. 9.5 - A thin elliptical plate has a mass m. Determine...Ch. 9.5 - The parabolic spandrel shown was cut from a thin,...Ch. 9.5 - Prob. 9.115PCh. 9.5 - Fig. P9.115 and P9.116 9.116 A piece of thin,...Ch. 9.5 - A thin plate of mass m is cut in the shape of an...Ch. 9.5 - Fig. P9.117 and P9.118 9.118 A thin plate of mass...Ch. 9.5 - Determine by direct integration the mass moment of...Ch. 9.5 - The area shown is revolved about the x axis to...Ch. 9.5 - The area shown is revolved about the x axis to...Ch. 9.5 - Determine by direct integration the mass moment of...Ch. 9.5 - Fig. P9.122 and P9.123 9.123 Determine by direct...Ch. 9.5 - Prob. 9.124PCh. 9.5 - Prob. 9.125PCh. 9.5 - Prob. 9.126PCh. 9.5 - Prob. 9.127PCh. 9.5 - Prob. 9.128PCh. 9.5 - Prob. 9.129PCh. 9.5 - Knowing that the thin cylindrical shell shown has...Ch. 9.5 - A circular hole of radius r is to be drilled...Ch. 9.5 - The cups and the arms of an anemometer are...Ch. 9.5 - Prob. 9.133PCh. 9.5 - Determine the mass moment of inertia of the 0.9-lb...Ch. 9.5 - Prob. 9.135PCh. 9.5 - Prob. 9.136PCh. 9.5 - A 2-mm thick piece of sheet steel is cut and bent...Ch. 9.5 - A section of sheet steel 0.03 in. thick is cut and...Ch. 9.5 - A corner reflector for tracking by radar has two...Ch. 9.5 - A farmer constructs a trough by welding a...Ch. 9.5 - The machine element shown is fabricated from...Ch. 9.5 - Determine the mass moments of inertia and the...Ch. 9.5 - Determine the mass moment of inertia of the steel...Ch. 9.5 - Prob. 9.144PCh. 9.5 - Determine the mass moment of inertia of the steel...Ch. 9.5 - Aluminum wire with a weight per unit length of...Ch. 9.5 - The figure shown is formed of 18-in.-diameter...Ch. 9.5 - A homogeneous wire with a mass per unit length of...Ch. 9.6 - Determine the mass products of inertia Ixy, Iyz,...Ch. 9.6 - Determine the mass products of inertia Ixy, Iyz,...Ch. 9.6 - Determine the mass products of inertia Ixy, Iyz,...Ch. 9.6 - Determine the mass products of inertia Ixy, Iyz,...Ch. 9.6 - 9.153 through 9.156 A section of sheet steel 2 mm...Ch. 9.6 - Prob. 9.154PCh. 9.6 - Prob. 9.155PCh. 9.6 - 9.153 through 9.156 A section of sheet steel 2 mm...Ch. 9.6 - Prob. 9.157PCh. 9.6 - Prob. 9.158PCh. 9.6 - Prob. 9.159PCh. 9.6 - Prob. 9.160PCh. 9.6 - Prob. 9.161PCh. 9.6 - For the homogeneous tetrahedron of mass m shown,...Ch. 9.6 - Prob. 9.163PCh. 9.6 - Prob. 9.164PCh. 9.6 - Prob. 9.165PCh. 9.6 - Determine the mass moment of inertia of the steel...Ch. 9.6 - Prob. 9.167PCh. 9.6 - Prob. 9.168PCh. 9.6 - Prob. 9.169PCh. 9.6 - 9.170 through 9.172 For the wire figure of the...Ch. 9.6 - Prob. 9.171PCh. 9.6 - Prob. 9.172PCh. 9.6 - Prob. 9.173PCh. 9.6 - Prob. 9.174PCh. 9.6 - Prob. 9.175PCh. 9.6 - Prob. 9.176PCh. 9.6 - Prob. 9.177PCh. 9.6 - Prob. 9.178PCh. 9.6 - Prob. 9.179PCh. 9.6 - Prob. 9.180PCh. 9.6 - Prob. 9.181PCh. 9.6 - Prob. 9.182PCh. 9.6 - Prob. 9.183PCh. 9.6 - Prob. 9.184PCh. 9 - Determine by direct integration the moments of...Ch. 9 - Determine the moment of inertia and the radius of...Ch. 9 - Prob. 9.187RPCh. 9 - Prob. 9.188RPCh. 9 - Prob. 9.189RPCh. 9 - Two L4 4 12-in. angles are welded to a steel...Ch. 9 - Prob. 9.191RPCh. 9 - Prob. 9.192RPCh. 9 - Prob. 9.193RPCh. 9 - Prob. 9.194RPCh. 9 - Prob. 9.195RPCh. 9 - Determine the mass moment of inertia of the steel...
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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY