10-13 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=0.40\ut{kg}\\ a&=30\ut{cm}=0.3\ut{m}\\ b&=50\ut{cm}=0.5\ut{m}\\ \omega&=5.0\ut{rad/s}\\ \end{cases} $$ $$ \begin{cases} m_1&=m, ~~{r_1}^2=b^2-a^2\\ m_2&=2m, ~~ {r_2}^2=a^2\\ m_3&=2m, ~~ {r_3}^2=a^2\\ \end{cases} $$ $$I=m{r}^2$$, $$ \begin{cases} I_1&=m(b^2-a^2)\\ I_2&=2ma^2\\ I_3&=2ma^2\\ \end{cases} $$ $$ \begin{aligned} I&=\Sigma I\\ &=m(3a^2+b^2) \end{aligned} $$ $$ \put \begin{cases} \RE : \text{Rotational Kinetic Energy}\\ \end{cases} $$ $$ \begin{aligned} W&=\Delta \RE\\ &=\frac{1}{2}I\omega^2\\ &=\frac{1}{2}m(3a^2+b^2)\omega^2\\ &=\frac{13}{5}\ut{J}\\ &=2.6\ut{J}\\ \end{aligned} $$