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 16.3 - Rotation about a Fixed Axis - Problems - Page 332: 13


$\omega_B=180rad/s$ $\omega_C=360rad/s$

Work Step by Step

The required angular velocity can be determined as follows: $v_P=\omega_A r_A=60(0.075)=4.5m/s$ Now $\omega_B=\frac{v_P}{r_D}$ We plug in the known values to obtain: $\omega_B=\frac{4.5}{0.025}=180rad/s$ Similarly, $v_{P^{\prime}}=\omega_Br_B$ $v_{P^{\prime}}=(180)(0.1)=18m/s$ and $\omega_C=\frac{v_{P^{\prime}}}{r_C}$ We plug in the known values to obtain: $\omega_C=\frac{18}{0.05}$ $\implies \omega_C=360rad/s$
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