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 333: 20

Answer

$ \omega_B=12 rad/s \circlearrowleft$

Work Step by Step

We can determine the required angular velocity as follows: $\alpha=\frac{d\omega}{dt}$ $\implies d\omega=\alpha dt$ $\implies \int_{\omega_{\circ}}^{\omega_A}=\int_0^t \alpha_A dt=\int_0^t 4t^3dt$ This simplifies to: $\omega_A=t^4+20$ We plug in the known values to obtain: $\omega_A=(2)^4+20=36rad/s$ We know that $\omega_B r_B=\omega_A r_A$ This can be rearranged as: $\omega_B=\frac{r_A}{r_B}\omega_A$ We plug in the known values to obtain: $\omega_B=\frac{0.15}{0.05}(36)$ $\implies \omega_B=12 rad/s \circlearrowleft$
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