11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

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In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

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Textbook Question

Chapter 18.3, Problem 18.143P

Consider a rigid body of arbitrary shape that is attached at its mass center O and subjected to no force other than its weight and the reaction of the support at O.

(a) Prove that the angular momentum H_O of the body about the fixed point O is constant in magnitude and direction, that the kinetic energy T of the body is constant, and that the projection along H_O of the angular velocity ω of the body is constant.

(b) Show that the tip of the vector ω describes a curve on a fixed plane in space (called the invariable plane), which is perpendicular to H_O and at a distance 2T/H_O from O.

(c) Show that with respect to a frame of reference attached to the body and coinciding with its principal axes of inertia, the tip of the vector ω appears to describe a curve on an ellipsoid of equation

I x ω x 2 + I y ω y 2 + I z ω z 2 = 2 T = constant

The ellipsoid (called the Poinsot ellipsoid) is rigidly attached to the body and is of the same shape as the ellipsoid of inertia, but of a different size.

Chapter 18.3, Problem 18.143P, Consider a rigid body of arbitrary shape that is attached at its mass center O and subjected to no

Fig. P18.143

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Chapter 18.3, Problem 18.142P

Chapter 18.3, Problem 18.144P

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Chapter 18 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - 18.3 Two uniform rods AB and CE, each of weight 3...Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Prob. 18.11P

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