dynamics-book-solutions

dynamics-book-solutions - DYNAMICS OF PARTICLES AND RIGID...

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DYNAMICS OF PARTICLES AND RIGID BODIES: A SYSTEMATIC APPROACH SOLUTION MANUAL TO TEXTBOOK PROBLEMS ANIL V. RAO Department of Aerospace & Mechanical Engineering Boston University
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ii Anil V. Rao Department of Aerospace & Mechanical Engineering Boston University 110 Cummington Street Boston, MA 02215 Copyright c ± 2004 Anil Vithala Rao. All Rights Reserved. This solution manual may not be reproduced in part or in whole without the expressed written consent of Anil Vithala Rao. Image on Cover Page Used with Permission via Unlimited Royalty-Free License from Foto Search Stock Footage and Stock Photography, 21155 Watertown Road, Waukesha, WI 53186-1898, USA. The drawings in this solution manual were created using CorelDraw R ± Versions 11 and 12. CorelDraw R ± is a Registered Trademark of The Corel TM Corporation, 1600 Carling Avenue, Ottawa, Ontario K1Z 8R7, Canada. This solution manual was typeset using the MiKTeX version of L A T E X2 ε and the Lucida R ± Bright Math, Lucida New Math, and Lucida Bright Expert fonts manu- factured by Y&Y, Inc., 106 Indian Hill, Carlisle, Massachusetts 01741, USA.
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Contents 2 Kinematics 1 Ques t ion2–1 . .................................... 1 t ion2–2 . 3 t ion2–3 . 6 t ion2–4 . 9 t ion2–5 . 11 t ion2–8 . 13 t ion2–9 . 18 Question 2–10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Question 2–11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Question 2–13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Question 2–15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Question 2–16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Question 2–17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Question 2–19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Question 2–20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Question 2–21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Question 2–23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3 Kinetics of Particles 61 t ion3–1 . 61 t ion3–2 . 68 t ion3–3 . 71 t ion3–5 . 80 t ion3–7 . 87 t ion3–9 . 92 Question 3–10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Question 3–11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Question 3–12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Question 3–13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Question 3–17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Question 3–19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Question 3–20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
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iv Contents Question 3–22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Question 3–23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Question 3–25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4 Kinetics of a System of Particles 147 Ques t ion4–1 . .................................... 147 t ion4–2 . 154 t ion4–3 . 158 t ion4–8 . 165 Question 4–17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5 Kinetics of Rigid Bodies 179 t ion5–1 . 179 t ion5–2 . 185 t ion5–3 . 193 t ion5–4 . 199 t ion5–5 . 204 t ion5–6 . 214 t ion5–7 . 220 t ion5–8 . 225 Question 5–10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Question 5–11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Question 5–12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Question 5–17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Question 5–20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
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Chapter 2 Kinematics Question 2–1 Abug B crawls radially outward at constant speed v 0 from the center of a ro- tating disk as shown in Fig. P2-1. Knowing that the disk rotates about its cen- ter O with constant absolute angular velocity Ω relative to the ground (where k Ω k= Ω ), determine the velocity and acceleration of the bug as viewed by an observer ±xed to the ground. r v 0 B O Ω Figure P2-1 Solution to Question 2–1 For this problem it is convenient to choose a ±xed reference frame F and a non- inertial reference frame A that is ±xed in the disk. Corresponding to reference frame F we choose the following coordinate system: Origin at Point O E x = Along OB at Time t = 0 E z = Out of Page E y = E z × E x
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2 Chapter 2. Kinematics Corresponding to the reference frame A that is Fxed in the disk, we choose the following coordinate system Origin at Point O e x = Along OB e z = Out of Page ( = E z ) e y = e z × e x The position of the bug is then resolved in the basis { e x , e y , e z } as r = r e x (2.1) Now, since the platform rotates about the e z
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This note was uploaded on 09/30/2011 for the course EGM 3401 taught by Professor Carlcrane during the Summer '08 term at University of Florida.

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dynamics-book-solutions - DYNAMICS OF PARTICLES AND RIGID...

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