Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 19 - Planar Kinetics of a Rigid Body: Impulse and Momentum - Section 19.2 - Principle of Impulse and Momentum - Problems - Page 538: 24



Work Step by Step

The angular velocity required can be determined as follows: According to the principle of impulse and momentum $I_{\circ}\omega_1+\Sigma\int_{t_1}^{t_2}M_Adt=I_{\circ}\omega_2+mv_{A_2}r$ [eq(1)] We know that $I_{\circ}=mk_{\circ}^2=30(0.125)^2=0.4688Kg\cdot m^2$ and $\omega_1=0$ $\omega_2=\frac{v_{\circ 2}}{r}=\frac{v_{O_2}}{0.15}$ This can be rearranged as: $v_{O_2}=0.15\omega_2$ Similarly $\Sigma\int_{t_1}^{t_2}M_Adt=\int_{0}^{4} 0.15\times 20tdt=24N\cdot s$ We plug in the known values in eq(1) to obtain: $0+24=0.4688\omega_2+30(0.15)(0.15\omega_2)$ This simplifies to: $\omega_2=21.0~rad/s$
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