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: 97


$\omega_S=57.5rad/s \circlearrowleft$ $\omega_{OA}=10.6 rad/s\circlearrowleft$

Work Step by Step

We can determine the required angular velocity as follows: $\frac{0.5}{0.1-x}=\frac{0.75}{x}$ This simplifies to: $x=0.01304m$ We know that $\omega_S=\frac{r_{O/H}}{x}\omega_H$ We plug in the known values to obtain: $\omega_S=\frac{0.15}{0.01304}(5)$ This simplifies to: $\omega_S=57.5rad/s \circlearrowleft$ We know that $v_A=\omega_S(r_A-x)$ $\implies v_A=57.5(0.05-0.01304)=2.125m/s$ and $v_A=\omega_{OA} r_{OA}$ This can be rearranged as: $\omega_{OA}=\frac{2.125}{0.2}=10.6 rad/s\circlearrowleft$
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