10-12 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} L_1&=35\ut{cm}=0.35\ut{m}\\ L_2&=95\ut{cm}=0.95\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$I=\Sigma mr^2,$$ $$ \begin{cases} I_1&=m{L_1}^2\\ I_2&=m{L_2}^2\\ \end{cases} $$ $$ \begin{aligned} I&=m({L_1}^2+{L_2}^2)\\ \end{aligned} $$ $$\ab{a,b}$$ $$\Sigma \tau = I \alpha,$$ $$ \begin{aligned} \alpha_1 &= \alpha_2\\ &= \frac{\Sigma \tau}{I}\\ &= \frac{L_1mg-L_2mg}{m({L_1}^2+{L_2}^2)}\\ &= \frac{L_1-L_2}{{L_1}^2+{L_2}^2}g\\ &=-\frac{24}{41}g\\ &\approx -5.740478048780488\ut{rad/s^2}\\ &\approx -5.7\ut{rad/s^2}\\ \end{aligned} $$ $$\alpha \approx 5.7\ut{rad/s^2}$$