VECTOR MECH....F/ENGNRS-STATICS -CONNECT
12th Edition
ISBN: 9781260689495
Author: BEER
Publisher: MCG CUSTOM
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Chapter 9.2, Problem 9.45P
9.45 and 9.46 Determine the polar moment of inertia of the area shown with respect to (a) point O, (b) the centroid of the area.
Fig. P9.45
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Determine the polar moment of inertia of the area shown with respect to (a) point , (b) the centroid of the area.
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Chapter 9 Solutions
VECTOR MECH....F/ENGNRS-STATICS -CONNECT
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 - 9.5 through 9.8 Determine by direct integration...Ch. 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 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - 9.12 through 9.14 Determine by direct integration...Ch. 9.1 - Prob. 9.13PCh. 9.1 - 9.12 through 9.14 Determine by direct integration...Ch. 9.1 - 9.15 and 9.16 Determine the moment of inertia and...Ch. 9.1 - Prob. 9.16PCh. 9.1 - 9.17 and 9.18 Determine the moment of inertia and...Ch. 9.1 - Prob. 9.18PCh. 9.1 - Determine the moment of inertia and the radius of...Ch. 9.1 - Prob. 9.20PCh. 9.1 - Prob. 9.21PCh. 9.1 - Determine the polar moment of inertia and the...Ch. 9.1 - 9.23 and 9.24 Determine the polar moment of...Ch. 9.1 - 9.23 and 9.24 Determine the polar moment of...Ch. 9.1 - (a) Determine by direct integration the polar...Ch. 9.1 - (a) Show that the polar radius of gyration kQ of...Ch. 9.1 - Determine the polar moment of inertia and the...Ch. 9.1 - Determine the polar moment of inertia and the...Ch. 9.1 - Using the polar moment of inertia of the isosceles...Ch. 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 - Prob. 9.35PCh. 9.2 - Determine the moments of inertia of the shaded...Ch. 9.2 - Prob. 9.37PCh. 9.2 - Fig. P9.37 and P9.38 9.38 Knowing that the shaded...Ch. 9.2 - Prob. 9.39PCh. 9.2 - Fig. P9.39 and P9.40 9.40 The polar moments of...Ch. 9.2 - Prob. 9.41PCh. 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 - 9.41 through 9.44 Determine the moments of inertia...Ch. 9.2 - 9.45 and 9.46 Determine the polar moment of...Ch. 9.2 - 9.45 and 9.46 Determine the polar moment of...Ch. 9.2 - Prob. 9.47PCh. 9.2 - Prob. 9.48PCh. 9.2 - Prob. 9.49PCh. 9.2 - Prob. 9.50PCh. 9.2 - Four L3 3 14 - in. angles are welded to a rolled...Ch. 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 - The strength of the rolled W section shown is...Ch. 9.2 - Two L76 76 6.4-mm angles are welded to a C250 ...Ch. 9.2 - Two steel plates are welded to a rolled W section...Ch. 9.2 - 9.57 and 9.58 The panel shown forms the end of a...Ch. 9.2 - 9.57 and 9.58 The panel shown forms the end of a...Ch. 9.2 - 9.59 and 9.60 The panel shown forms the end of a...Ch. 9.2 - 9.59 and 9.60 The panel shown forms the end of a...Ch. 9.2 - A vertical trapezoidal gate that is used as an...Ch. 9.2 - The cover for a 0.5-m-diameter access hole in a...Ch. 9.2 - Determine the x coordinate of the centroid of the...Ch. 9.2 - Determine the x coordinate of the centroid of the...Ch. 9.2 - Show that the system of hydrostatic forces acting...Ch. 9.2 - Show that the resultant of the hydrostatic forces...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 - 9.67 through 9.70 Determine by direct integration...Ch. 9.3 - Prob. 9.70PCh. 9.3 - 9.71 through 9.74 Using the parallel-axis theorem,...Ch. 9.3 - 9.71 through 9.74 Using the parallel-axis theorem,...Ch. 9.3 - 9.71 through 9.74 Using the parallel-axis theorem,...Ch. 9.3 - Prob. 9.74PCh. 9.3 - 9.75 through 9.78 Using the parallel-axis theorem,...Ch. 9.3 - 9.75 through 9.78 Using the parallel-axis theorem,...Ch. 9.3 - 9.75 through 9.78 Using the parallel-axis theorem,...Ch. 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 - 9.86 through 9.88 For the area indicated,...Ch. 9.3 - 9.86 through 9.88 For the area indicated,...Ch. 9.3 - 9.89 and 9.90 For the angle cross section...Ch. 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 - 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 - Using Mohrs circle, determine the moments of...Ch. 9.4 - For the quarter ellipse of Prob. 9.67, use Mohrs...Ch. 9.4 - Prob. 9.98PCh. 9.4 - 9.98 though 9.102 Using Mohrs circle, determine...Ch. 9.4 - 9.98 though 9.102 Using Mohrs circle, determine...Ch. 9.4 - 9.98 through 9.102 Using Mohrs circle, determine...Ch. 9.4 - 9.98 through 9.102 Using Mohrs circle, determine...Ch. 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 - Prob. 9.106PCh. 9.4 - it is known that for a given area Iy = 48 106 mm4...Ch. 9.4 - Prob. 9.108PCh. 9.4 - Using Mohrs circle, prove that the expression...Ch. 9.4 - Using the invariance property established in the...Ch. 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 - A thin plate of mass m is cut in the shape of an...Ch. 9.5 - Prob. 9.118PCh. 9.5 - Prob. 9.119PCh. 9.5 - The area shown is revolved about the x axis to...Ch. 9.5 - Prob. 9.121PCh. 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 - Determine by direct integration the mass moment of...Ch. 9.5 - Prob. 9.125PCh. 9.5 - A thin steel wire is bent into the shape shown....Ch. 9.5 - Shown is the cross section of an idler roller....Ch. 9.5 - Shown is the cross section of a molded flat-belt...Ch. 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 - Prob. 9.132PCh. 9.5 - After a period of use, one of the blades of a...Ch. 9.5 - Determine the mass moment of inertia of the 0.9-lb...Ch. 9.5 - 9.135 and 9.136 A 2-mm thick piece of sheet steel...Ch. 9.5 - 9.135 and 9.136 A 2 -mm thick piece of sheet steel...Ch. 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 - Prob. 9.140PCh. 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 - Fig. P9.143 and P9.144 9.144 Determine the mass...Ch. 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 - Prob. 9.153PCh. 9.6 - Prob. 9.154PCh. 9.6 - 9.153 through 9.156 A section of sheet steel 2 mm...Ch. 9.6 - 9.153 through 9.156 A section of sheet steel 2 mm...Ch. 9.6 - The figure shown is formed of 1.5-mm-diameter...Ch. 9.6 - Prob. 9.158PCh. 9.6 - 9.159 and 9.160 Brass wire with a weight per unit...Ch. 9.6 - Fig. P9.160 9.159 and 9.160 Brass wire with a...Ch. 9.6 - Complete the derivation of Eqs. (9.47) that...Ch. 9.6 - Prob. 9.162PCh. 9.6 - Prob. 9.163PCh. 9.6 - Prob. 9.164PCh. 9.6 - Shown is the machine element of Prob. 9.141....Ch. 9.6 - Determine the mass moment of inertia of the steel...Ch. 9.6 - The thin, bent plate shown is of uniform density...Ch. 9.6 - A piece of sheet steel with thickness t and...Ch. 9.6 - Determine the mass moment of inertia of the...Ch. 9.6 - 9.170 through 9.172 For the wire figure of the...Ch. 9.6 - Prob. 9.171PCh. 9.6 - 9.172 Prob. 9.146 9.146 Aluminum wire with a...Ch. 9.6 - For the homogeneous circular cylinder shown with...Ch. 9.6 - For the rectangular prism shown, determine the...Ch. 9.6 - Prob. 9.175PCh. 9.6 - Prob. 9.176PCh. 9.6 - Consider a cube with mass m and side a. (a) Show...Ch. 9.6 - Prob. 9.178PCh. 9.6 - Prob. 9.179PCh. 9.6 - 9.180 through 9.184 For the component described in...Ch. 9.6 - 9.180 through 9.184 For the component described in...Ch. 9.6 - Prob. 9.182PCh. 9.6 - 9.180 through 9.184 For the component described in...Ch. 9.6 - 9.180 through 9.184 For the component described in...Ch. 9 - Determine by direct integration the moments of...Ch. 9 - Determine the moment of inertia and the radius of...Ch. 9 - Determine the moment of inertia and the radius of...Ch. 9 - Determine the moments of inertia Ix and Iy of the...Ch. 9 - Determine the polar moment of inertia of the area...Ch. 9 - Two L4 4 12-in. angles are welded to a steel...Ch. 9 - Using the parallel-axis theorem, determine the...Ch. 9 - Prob. 9.192RPCh. 9 - Fig. P9.193 and P9.194 9.193 A thin plate with a...Ch. 9 - Fig. P9.193 and P9.194 9.194 A thin plate with...Ch. 9 - A 2-mm-thick piece of sheet steel is cut and bent...Ch. 9 - Determine the mass moment of inertia of the steel...
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- (a) Determine by direct integration the polar moment of inertia of the annular area shown. (b) Using the result of part a, determine the moment of inertia of the given area with respect to the x axis.Fig. P9.18arrow_forwardFor the entire section shown, the moments of inertia with respect to the centroidal x and y axes at point C are Ix = 0.162(106) mm4 and Iy = 0.454(106) mm4, respectively. a. Determine the product of inertia with respect to the centroid at C, in mm4. b. Use a Mohr's Circle to determine the orientation (in degrees) of the principal axes of the section about the centroid C. c. Use the same Mohr's Circle to determine the values of the principal moments of inertia about the centroid C, in mm4.arrow_forward1.3 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_forward
- Determine the moments of inertia and the product of inertia of the L3 x 2 x 1/4-14 angle cross section of Prob. 9.74 with respect to new centroidal axes obtained by rotating the x and y axes 30° clockwise.(Reference to Problem 9.75):Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.arrow_forwardUsing Mohr’s circle, determine for the quarter ellipse of Prob. 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the x and y axes about O (a) through 45° counterclockwise, (b) through 30° clockwise.(Reference to Problem 9.67):Determine by direct integration the product of inertia of the given area with respect to the x and y axes.arrow_forward9.31 and 9.32 Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis. 2 in. 2 in. 3 in. -3 in.+ 1 in. 3 in. 2 in. 2 in. 3 in. 1 in. 1 in.- -1 in. Fig. P9.32.arrow_forward
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- Problem 09.086 - Orientation of the principal axes and the corresponding moments of inertia For the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia when b= 76 mm and h = 56 mm. b The value of mis The value of 0m2 is The value of Imax is The value of I min is 180 270 1.429 7292 × h x 106 mm4. 106 mm4arrow_forwardHELP ME PLEASE THANK YOUarrow_forwardb. X A very common structural component of an aircraft wing is its spar. An 'I' shaped spar is shown in Fig. 1b. Locate the centroid of the section from X- X as shown in Fig. 1b and determine the area moment of inertia of this '1'- shaped spar about the centroid for x-axis. 100 200 T 300 Fig. 1b 10 All dimensions in mm 10 Xarrow_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