Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.194RP
(a)
To determine
Find the mass moment of inertia of the plate with respect to the y axis.
(b)
To determine
Find the axis
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A 2-mm-thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass moment of inertia of the component with respect to each of the coordinate axes.
Chapter 9 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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 - Prob. 9.3PCh. 9.1 - Prob. 9.4PCh. 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. 9.7PCh. 9.1 - Prob. 9.8PCh. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P
Ch. 9.1 - Prob. 9.11PCh. 9.1 - Prob. 9.12PCh. 9.1 - Prob. 9.13PCh. 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 - Prob. 9.19PCh. 9.1 - Prob. 9.20PCh. 9.1 - Prob. 9.21PCh. 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 - Prob. 9.31PCh. 9.2 - Prob. 9.32PCh. 9.2 - Prob. 9.33PCh. 9.2 - Prob. 9.34PCh. 9.2 - Prob. 9.35PCh. 9.2 - Prob. 9.36PCh. 9.2 - Prob. 9.37PCh. 9.2 - Prob. 9.38PCh. 9.2 - Prob. 9.39PCh. 9.2 - Prob. 9.40PCh. 9.2 - Prob. 9.41PCh. 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 - Prob. 9.47PCh. 9.2 - 9.47 and 9.48 Determine the polar moment of...Ch. 9.2 - 9.49 Two channels and two plates are used to form...Ch. 9.2 - Prob. 9.50PCh. 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 - 9.60 The panel shown forms the end of a trough...Ch. 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 - Prob. 9.68PCh. 9.3 - Prob. 9.69PCh. 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 - Prob. 9.113PCh. 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 - 9.117 A thin plate with a mass m has the...Ch. 9.5 - Prob. 9.118PCh. 9.5 - 9.119 Determine by direct integration the mass...Ch. 9.5 - The area shown is revolved about the x axis to...Ch. 9.5 - 9.121 The area shown is revolved about the x axis...Ch. 9.5 - Prob. 9.122PCh. 9.5 - Prob. 9.123PCh. 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 - Prob. 9.130PCh. 9.5 - Prob. 9.131PCh. 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 - Prob. 9.137PCh. 9.5 - A section of sheet steel 0.03 in. thick is cut and...Ch. 9.5 - Prob. 9.139PCh. 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 - Prob. 9.151PCh. 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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- Please help me answer the following, thanks.arrow_forwardFig. PB.15 B.15 A thin steel wire is bent into the shape shown. Dennting the mass per unit length of the wire by m', determine by direct integration the mo- ment of inertia of the wire with respect to each of the coordinate aves. y=(23_123)32arrow_forwardA thin, semielliptical plate has a mass m . Determine the mass moment of inertia of the plate with respect to (a) the centroidal axis BB, (b) the centroidal axis CC ’ that is perpendicular to the plate.arrow_forward
- 1.3 cm 1.0 cm -0.5 cm 3.8 cm 0.5 cm AI B 3.6 cm PROBLEM 9.44 Determine the moments of inertia I, and I, of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.arrow_forwardFor items 4 and 5. A thin rectangular plate is welded on the center of the top of a circular cylinder. The mass of the cylinder is 5kg and the mass of the triangular plate is 2kg. Note that the x-axis is located on the centroidal x-axis of the triangular plate. 30cm 26cm 0.1725 m diam. d=7cm X 10cm 4. Which of the following is closest to the moment of inertia of the composite object about the x- axis? 0.208 kg-m^2 5. Which of the following is closest to the radius of gyration of the composite object about the x- axis?arrow_forward18.107 Determine the moment of inertia of the object described in Problem 18.106 about the axis through the center of mass of the object parallel to Lo- 20 mm Ο 10 mm Lo -100 mm. Problems 18.106/18.107 30 mmarrow_forward
- Determine the mass moment of inertia of a ring of mass m, cut from a thin uniform plate, with respect to (a) the axis AA', (b) the centroidal axis CC' that is perpendicular to the plane of the ring.arrow_forward! Required information Problem 09.141 - Mass moment of inertia of machine elements NOTE: This is a multi-part question. The machine element shown is fabricated from steel, where h = 64 mm. The density of steel is 7850 kg/m³. 20 mm 40 mm 80 mm 40 mm -20 mm 40 mm Problem 09.141.b - Mass moment of inertia of machine elements Determine the mass moment of inertia of the assembly with respect to the y axis. The mass moment of inertia of the assembly with respect to the y axis is 22.9 ✪ × 10-³ kg.m². Xarrow_forwardFor the component described in the problem indicated, determine (a) the principal mass moments of inertia at the origin, (b) the principal axes of inertia at the origin. Sketch the body and show the orientation of the principal axes of inertia relative to the x, y, and z axes.Prob. 9.141Reference to Problem 9.141:arrow_forward
- A thin plate with a mass m is cut in the shape of an equilateral triangle of side a . Determine the mass moment of inertia of the plate with respect to (a) the centroidal axes AA' and BB',(b) the centroidal axis CC ’ that is perpendicular to the plate.arrow_forwardUsing the polar moment of inertia of the isosceles triangle of Prob. 9.28, show that the centroidal polar moment of inertia of a circular area of radius r is π4/2. ( Hint: As a circular area is divided into an increasing number of equal circular sectors, what is the approximate shape of each circular sector?)(Reference to Problem 9.28):Determine the polar moment of inertia and the polar radius of gyration of the isosceles triangle shown with respect to point O.arrow_forward. The thin plate shown is composed of a rectangular plate of mass 102 kg and a quarter-circular plate of mass 60 kg. Which of the following best pproximates the mass moment of inertia of the shape about the x-axis? ´r = 1.500 m 3.00 marrow_forward
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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY