11-48 할리데이 11판 솔루션 일반물리학

$$\begin{cases} I_A&=3.30\ut{kg\cdot m^2}\\ \omega_{Ai}&=450\ut{rev/min}\\ I_B&=6.60\ut{kg\cdot m^2}=2I_A\\ \omega_{Bi}&=900\ut{rev/min}=2\omega_{Ai}\\ \end{cases}$$ $$\Delta \Sigma \vec L=0,$$ $$\begin{aligned} 0&=\Delta \Sigma \br{I\omega}\\ &=\Sigma \br{I\omega_f}-\Sigma \br{I\omega_i}\\ &=\omega_f\Sigma {I}-\Sigma \br{I\omega_i}\\ \end{aligned}$$ $$\omega_f={\Sigma \br{I\omega_i}\over\Sigma {I} }$$ $$\ab{a}$$ $$\begin{aligned} \omega_f&={{I_A\omega_{Ai}+I_B\omega_{Bi}}\over I_A+I_B }\\ &={{I_A\omega_{Ai}+(2I_A)(2\omega_{Ai})}\over I_A+(2I_A) }\\ &={5\over 3 }\omega_{Ai}\\ &=750\ut{rev/min}\\ \end{aligned}$$ $$\ab{b,c}$$ $$\begin{cases} I_C&=6.60\ut{kg\cdot m^2}=2I_A\\ \omega_{Ci}&=-800\ut{rev/min} \end{cases}$$ $$\begin{aligned} \vec \omega_f &={{I_A\omega_{Ai}+I_C\omega_{Ci}}\over I_A+I_C }\\ &=-{1150\over 3}\ut{rev/min}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} \omega_f &\approx 383.3333333333333\ut{rev/min}\\ &\approx 383\ut{rev/min}\\ \end{aligned}$$ $$\ab{c}$$ $$\vec \omega \lt 0 \Harr \text{Clockwise}$$