# Chapter 19 - Planar Kinetics of a Rigid Body: Impulse and Momentum - Section 19.2 - Principle of Impulse and Momentum - Problems - Page 535: 9

$\omega_2=103~ rad/s$

#### Work Step by Step

The required angular velocity can be determined as follows: We know that $I_{\circ}\omega_1+\Sigma \int_{t_1}^{t_2} M_{\circ} dt=I_{\circ}\omega_2~~~$[eq(1)] As $I_{\circ}=\frac{1}{2}mr^2$ $\implies I_{\circ}=\frac{1}{2}(\frac{10}{32.2})(0.5)^2=0.0388slug\cdot ft^2$ and $\omega_1=0$ Now $\int_{t_1}^{t_2}M_{\circ}=Prt=2(0.5)(4)=4lb\cdot ft/s$ We plug in the known values in eq(1) to obtain: $0+4=(0.0388)\omega_2$ This simplifies to: $\omega_2=103~ rad/s$

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