11-57 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=31\ut{g}\\ d&=15\ut{cm}\\ \omega &= 0.85\ut{rad/s}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Sigma I &=I_A+I_B+I_C\\ &=m{R_A}^2+m{R_B}^2+m{R_C}^2\\ &=m\bra{{d}^2+\br{2d}^2+\br{3d}^2}\\ &=14md^2\\ &=9.765\times10^{-3}\ut{kg\cdot m^2}\\ &\approx 9.8\times10^{-3}\ut{kg\cdot m^2}\\ &\approx 9.8\ut{g\cdot m^2}\\ \end{aligned} $$ $$\ab{b}$$ $$L = I\omega,$$ $$ \begin{aligned} L_B &= I_B\omega\\ &= m\br{2d}^2\omega\\ &= 4md^2\omega\\ &=15.81\times10^{-3}\ut{kg\cdot m^2/s}\\ &\approx 16\times10^{-3}\ut{kg\cdot m^2/s}\\ &\approx 16\ut{g\cdot m^2/s}\\ \end{aligned} $$ $$\ab{c}$$ $$L = I\omega,$$ $$ \begin{aligned} \Sigma L &=\Sigma \br{I\omega}\\ &=\omega\Sigma {I}\\ &=\omega\br{14md^2}\\ &=14md^2\omega\\ &=55.335\times 10^{-3}\ut{kg\cdot m^2/s}\\ &\approx 55\times 10^{-3}\ut{kg\cdot m^2/s}\\ &\approx 55\ut{g\cdot m^2/s}\\ \end{aligned} $$