Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 16 - Planar Kinematics of a Rigid Body - Section 16.5 - Relative-Motion Analysis: Velocity - Problems - Page 356: 65


$\omega=20 rad/s$ $v_A=2ft/s$

Work Step by Step

The required velocity and angular velocity can be determined as follows: $v_{C/B}=v_C-v_B$ $\implies v_C=v_B+v_{C/B}$ $\implies v_C=v_B+\omega r_{C/B}$ We plug in the known values to obtain: $-4=8-0.6\omega$ This simplifies to: $\omega=20 rad/s$ Similarly, for rack $A$ and gear $B$, we know that $v_A=v_B+v_{A/B}$ $\implies v_A=v_B+\omega r_{A/B}$ We plug in the known values to obtain: $v_A=8-(20)(0.3)=2ft/s$
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