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 334: 24

Answer

$\omega_B=211 rad/s$

Work Step by Step

We can determine the required angular velocity as follows: $\int_0^{\omega_A}d\omega=\int_0^t \alpha dt$ $\int_0^{\omega_A}d\omega=\int_0^{1.5} 400 t^3 dt$ This simplifies to: $\omega_A=(\frac{400}{4}t^4)|_0^{1.5}$ $\implies \omega_A=506.25 rad/s$ As gear A and gear B are meshed together, therefore $\omega_A r_A=\omega_B r_B$ This can be rearranged as: $\omega_B=\frac{r_A}{r_B}\omega_A$ We plug in the known values to obtain: $\omega_B=(\frac{0.5}{1.5})(506.25)$ $\implies \omega_B=211 rad/s$
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