10-50 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=1.6\ut{kg}\\ L&=0.60\ut{m}\\ \theta&=30\degree\\ \omega&=1.2\ut{rad/s}\\ \end{cases} $$ $$ \begin{cases} m_1&=m_2=2m\\ m_3&=m\\ \end{cases} $$ $$ \put \begin{cases} \RE : \text{Rotational Kinetic Energy}\\ \end{cases} $$ $$\ab{a}$$ $$I=\Sigma mr^2,$$ $$ \begin{cases} r_1&=r_2=L\\ r_3&=2L\\ \end{cases} $$ $$ \begin{cases} I_{a1}&=I_{a2}=(2m)L^2=2mL^2\\ I_3&=m(2L)^2=4mL^2\\ \end{cases} $$ $$ \begin{aligned} I_a&=I_{a1}+I_{a2}+I_3\\ &=8mL^2 \end{aligned} $$ $$ \begin{aligned} \RE_a&=\frac{1}{2}I\omega^2\\ &=4mL^2\omega^2\\ &=\frac{10368}{3125}\ut{J}\\ &=3.31776\ut{J}\\ &\approx 3.3\ut{J}\\ \end{aligned} $$ $$\ab{b}$$ $$I=\Sigma mr^2,$$ $$ \begin{cases} r_1&=r_2=L\cos\theta\\ r_3&=2L\\ \end{cases} $$ $$ \begin{cases} I_{b1}&=I_{b2}=(2m)(L\cos\theta)^2\\ I_3&=m(2L)^2=4mL^2\\ \end{cases} $$ $$ \begin{aligned} I_b&=I_{b1}+I_{b2}+I_3\\ &=2 m L^2 \(\cos 2 \theta +3\)\\ \end{aligned} $$ $$ \begin{aligned} \RE_b&=\frac{1}{2}I\omega^2\\ &=mL^2\omega^2\(\cos 2 \theta +3\)\\ &=\frac{9072}{3125}\ut{J}\\ &=2.90304\ut{J}\\ &\approx 2.9\ut{J}\\ \end{aligned} $$