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# Chapter 20

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R.C. Hibbeler Engineering Mechanics Dynamics solution manual

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### Chapter 20

6. 6. 91962_11_s20_p0867-0924 6/8/09 5:05 PM Page 872 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 20–7. If the top gear B rotates at a constant rate of V , z determine the angular velocity of gear A, which is free to rotate about the shaft and rolls on the bottom fixed gear C. B rB ω A h2 O y h1 rC C x vP = vk * (-rB j) = vrB i Also, vP = vA * (-rB j + h2k) = 3 vAx vAz 3 i j k vAy 0 -rB h2 = (vAy h2 + vAz rB)i - (vAx h2)j - vAx rB k Thus, vrB = vAy h2 + vAz rB (1) 0 = vAx h2 0 = vAx rB vAx = 0 vR = 0 = 3 0 vAz 3 = ( -vAy h1 + vAz rC)i i j k vAy 0 -rC -h1 vAy = vAz a b rC h1 From Eq. (1) vrB = vAz c a b + rB d rC h2 h1 vAy = a ba b rB h1 v rC rB h1v vAz = ; rC h2 + rB h1 h1 rC h2 + rB h1 vA = a ba bj + a bk rC rB h1 v rB h1v Ans. h1 rC h2 + rB h1 rC h2 + rB h1 872