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 16.6 - Instantaneous Center of Zero Velocity - Problems - Page 372: 99


$\omega_{CD}=57.7rad/s \circlearrowleft$

Work Step by Step

We can determine the required angular velocity as follows: According to sine rule $\frac{r_{IC/B}}{sin90}=\frac{r_{IC/F}}{sin60}=\frac{r_{B/F}}{sin30}$ This simplifies to: $r_{IC/B}=\frac{r_{B/F}}{sin30}=\frac{0.3}{sin30}=0.6m$ $r_{IC/F}=0.6sin60=0.5196m$ and $\omega_{BF}=\frac{0.1}{0.6}(50)=8.333 rad/s$ Now $v_F=\omega_{BF}r_{IC/F}$ $\implies v_F=8.333(0.5196)=4.33m/s$ Similarly $v_F=\omega_{CD}r_{CF}$ This can be rearranged as: $\omega_{CD}=\frac{v_F}{r_{CF}}$ We plug in the known values to obtain: $\omega_{CD}=\frac{4.33}{0.075}=57.7rad/s \circlearrowleft$
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