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 357: 66


$v_O=0.667ft/s \rightarrow$

Work Step by Step

We can determine the required velocity as follows: We know that $v_{C/B}=v_C-v_B$ $\implies v_B=v_C\times \omega\times r_{B/C}$ $\implies 3\hat i=-4\hat i+(-\omega \hat k)\times (1.5+0.75\hat j)$ $\implies 3\hat i=(2.25\omega -4)\hat i$ This simplifies to: $\omega=3.111 rad/s$ Now the relative motion between points $O$ and $C$ is given as $v_O=v_C+v_{O/C}$ $\implies v_O=v_C+\omega \times r_{O/C}$ We plug in the known values to obtain: $v_O=-4\hat i+(-3.111\hat k)(1.5\hat j)$ This simplifies to: $v_O=0.667ft/s \rightarrow$
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