Engineering Mechanics: Statics & Dynamics (14th Edition)
Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 21.3, Problem 22P

If a body contains no planes of symmetry, the principal moments of inertia can be determined mathematically. To show how this is done, consider the rigid body which is spinning with an angular velocity ω, directed along one of its principal axes of inertia. If the principal moment of inertia about this axis is I, the angular momentum can be expressed as H = = x i + y j + z k. The components of H may also be expressed by Eqs. 21–10, where the inertia tensor is assumed to be known. Equate the i, j, and k components of both expressions for H and consider ωx, ωy, and ωz to be unknown. The solution of these three equations is obtained provided the determinant of the coefficients is zero. Show that this determinant, when expanded, yields the cubic equation

I3(Ixx + Iyy + Izz)I2

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Chapter 21 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY