11판/11. 굴림운동, 토크, 각운동량

11-30 할리데이 11판 솔루션 일반물리학

짱세디럭스 2024. 5. 18. 12:46
put {A:DiskB:ManC:Stone \put \begin{cases} A:\text{Disk}\\ B:\text{Man}\\ C:\text{Stone}\\ \end{cases} (a)\ab{a} ΔΣL=0,\Delta \Sigma \vec L=0, 0=ΣLi=ΣLf=LAf+LBf+LCf=IAωf+IBωf+rC×mCvC=ωf(IA+mBR2)+RmCvC \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} ωf=RmCvCIA+mBR2, \vec \omega_f=-{Rm_C\vec v_C\over I_A+m_BR^2}, ωAf=RmvI+MR2\omega_{Af}={Rmv\over I+MR^2} (b)\ab{b} v=rω,v=r\omega, vBf=R2mvI+MR2 \begin{aligned} v_{Bf}&={R^2mv\over I+MR^2} \end{aligned}