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 370: 87


$\omega_{BC}=8.66 rad/s \circlearrowleft$ $\omega_{AB}=4 rad/s \circlearrowright$

Work Step by Step

The required angular velocity can be determine as follows: $v_C=\omega_{CD} r_{CD}=4(0.5)=2m/s$ $v_B=\omega_{AB} r_{AB}=\omega_{AB}(1)=\omega_{AB}$ Similarly $r_{IC/B}=\frac{4}{cos30}=0.4619m$ and $r_{IC/C}=0.4tan30=0.231m$ We know that $v_C=\omega_{BC}r_{IC/C}=0.231\omega_{BC}$ This simplifies to: $\omega_{BC}=8.66 rad/s \circlearrowleft$ Similarly $v_B=\omega_{BC} r_{IC/B}$ We plug in the known values to obtain: $\omega_{AB}=(8.66)(0.4619)=4 rad/s \circlearrowright$
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