11-30 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} A:\text{Disk}\\ B:\text{Man}\\ C:\text{Stone}\\ \end{cases} $$ $$\ab{a}$$ $$\Delta \Sigma \vec L=0,$$ $$ \begin{aligned} 0&=\Sigma \vec L_i=\Sigma \vec L_f\\ &=\vec L_{Af}+\vec L_{Bf}+\vec L_{Cf}\\ &=I_A\vec \omega_f+I_B\vec \omega_f+\vec r_C\times m_C\vec v_C\\ &=\vec \omega_f\br{I_A+m_BR^2}+Rm_C\vec v_C\\ \end{aligned} $$ $$ \vec \omega_f=-{Rm_C\vec v_C\over I_A+m_BR^2},$$ $$\omega_{Af}={Rmv\over I+MR^2} $$ $$\ab{b}$$ $$v=r\omega,$$ $$ \begin{aligned} v_{Bf}&={R^2mv\over I+MR^2} \end{aligned} $$