11-18 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} A : \text{Man}\\ D : \text{Disk}\\ \end{cases} $$ $$ \begin{cases} m_D&=150\ut{kg}\\ r_i&=2.0\ut{m}\\ I_D&=300\ut{kg\cdot m^2}\\ m_A&=60\ut{kg}\\ \omega_i&=0.85\ut{rad/s}\\ r_f&=0.30\ut{m}\\ \end{cases} $$ $$I=mr^2,$$ $$\Delta \Sigma \vec L=0,$$ $$ \begin{aligned} 0&=\Delta (\vec L_D+\vec L_A)\\ &=(\vec L_{Df}+\vec L_{Af})-(\vec L_{Di}+\vec L_{Ai})\\ &=(I_D\omega_{f}+I_{Af}\omega_{f})-(I_D\omega_{i}+I_{Ai}\omega_{i})\\ &=(I_D+I_{Af})\omega_{f}-(I_D+I_{Ai})\omega_{i}\\ \end{aligned} $$ $$ \begin{aligned} \omega_f &=\frac{I_D+I_{Ai}}{I_D+I_{Af}}\omega_i\\ &=\frac{I_D+m_A{r_i}^2}{I_D+m_A{r_f}^2}\omega_i\\ &=\frac{900}{509}\omega_i\\ &=\frac{765}{509}\ut{rad/s}\\ &\approx 1.5029469548133596\ut{rad/s}\\ &\approx 1.5\ut{rad/s}\\ \end{aligned} $$