11-22 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} A : \text{Disk}\\ B : \text{Man}\\ C : \text{Ball}\\ \end{cases} $$ $$ \begin{cases} \omega_i&=0\\ m_B&=20\ut{kg}\\ R&=2.0\ut{m}\\ I_A&=150\ut{kg\cdot m^2}\\ m_C&=1.0\ut{kg}\\ v_{Ci}&=12\ut{m/s}\\ \phi&=37\degree\\ \end{cases} $$ $$ \begin{aligned} \omega&=\frac{v_t}{R},\\ &=\frac{v\cos\phi}{R}\taag1\\ \end{aligned} $$ $$ \begin{cases} I_B&=m_BR^2\\ I_C&=m_CR^2 \end{cases} $$ $$\Delta \Sigma \vec L=0,$$ $$ \begin{aligned} 0 &=\Delta(\vec L_A+\vec L_B)+\Delta\vec L_C\\ &=(\vec L_{Af}+\vec L_{Bf})+(\vec L_{Cf}-\vec L_{Ci})\\ &=\Sigma \vec L_{f}-\vec L_{Ci}\\ &=\vec \omega_f\Sigma I -I_C \vec\omega_{Ci}\\ \end{aligned} $$ $$ \begin{aligned} \vec \omega_f&=\frac{I_C}{\Sigma I}\omega_{Ci}\\ &=\frac{I_C}{\Sigma I}\cdot\frac{v_{Ci}\cos\phi}{R}\\ &=\frac{Rm_Cv_{Ci}\cos\phi}{\Sigma I}\\ &=\frac{4}{39}\cos37\degree\\ &\approx 8.19113343638249\times10^{-2}\ut{rad/s}\\ &\approx 8.2\times10^{-2}\ut{rad/s}\\ \end{aligned} $$