Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 21.1, Problem 1P
Show that the sum of the moments of inertia of a body, Ixx + Iyy + Izz, is independent of the orientation of the x, y, z axes and thus depends only on the location of the origin.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine the following statement that is true regarding Mohr's Circle.
Reference points on Mohr's Circle from two perpendicular axes on the cross-section can lie
at angles smaller than 180 degrees relative to each other.
Mohr's Circle can't be used to identify angles between principal and non-principal axes.
Mohr's Circle contains all possible moment of inertia and product of inertia values for a given
fixed area about all rotated axes around the same origin.
A reference point on Mohr's Circle that corresponds to one of the principal axes can lie at
coordinates of (492, 18.7).
The center of Mohr's Circle can only be calculated using principal moments of inertia.
Find the radius of gyration of the area in the first quadrant bounded by the lines y = 0, x = 3, and the curve x2 = 3y with respect to the y-axis.
2.32
3.10
О 3.22
О 3.43
Show using analytical methods how the mass moment of inertia changes for a
uniform rod by changing the axis about which it rotates.
Z
Figure 1 - Uniform Rod Q1
dr
L
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Determine the product of inertia with respect to the x- and y-axes for the quarter circular, thin ring (tR) by integration.arrow_forwardFind the moments of inertia (J1,J2) of a homogeneous ring of circular shape with respect to both axes. The mass and radius (m,R) of the ring are knownarrow_forwardDetermine the following statement that is true regarding Mohr's Circle. Mohr's Circle contains all possible moment of inertia and product of inertia values for a given fixed area about all rotated axes around the same origin. O A reference point on Mohr's Circle that corresponds to one of the principal axes can lie at coordinates of (492, 18.7). Reference points on Mohr's Circle from two perpendicular axes on the cross-section can lie at angles smaller than 180 degrees relative to each other. O The center of Mohr's Circle can only be calculated using principal moments of inertia. O Mohr's Circle can't be used to identify angles between principal and non-principal axes.arrow_forward
- Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume ho = 0.34h, bo = 0.16b. y | h h. b Answers: bh3 %3D ly = i hb3 Iz = i bh3 + i hb3arrow_forwardDetermine the moment of inertia of the shaded area about x-axis. Set h= 5.7 cm. 4h 2h 2991 cm^4 7741 cm^4 5806 cm^4 11436 cm^4 11260 cm^4arrow_forwardThe moments of inertia about the x- and u-axes of the plane region areIx = 14 × 10^9 mm^4 and Iu = 38 × 10^9 mm^4, respectively. If h = 200 mm, determine the area of the region, and the radius of gyration about the centroidal axis parallel to the x-axis.arrow_forward
- Y YI R a a image 1 barrow_forwardFind the moment of inertia with respect to the line x=2a the area bounded by x = a2/3 y1/3, the line x = 2a and the x-axis.arrow_forwardDetermine the moments of inertia about the centroidal x-axes of the trapezoidal area. a=147 mm; b=294 mm; h=441 mm. Answer the question in mm4. Yanıt: b b Yanıt: Answer the question in mm4. h Determine the moments of inertia about the centroidal y-axes of the trapezoidal area. X Warrow_forward
- Find the center of mass and the moment of inertia about the z-axis of a thin shell of constant density & cut from the cone x² + y² - z² =0 by the planes z = 2 and z = 5. The center of mass is the point Carrow_forwardFind the moment of inertia for the cross-sectional shape about the x and y axes, given the function: y = 2·x2 and L = 1.6 m.arrow_forwardDetermine the moments of inertia with respect to the centroidal axes of the following figure: 30 cm 15 cm 15 cm 7.5 cm 10 cm 10 cm Xarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY