11-8 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \cfrac{R_B}{R_A}&=4.00\\ \end{cases} $$ $$ \put \begin{cases} \RE : \text{Rotational Kinetic Energy}\\ \end{cases} $$ $$ \begin{aligned} v_A&=v_B\\ R_A\omega_A&=R_B\omega_B\\ \end{aligned} $$ $$ \begin{aligned} \frac{\omega_B}{\omega_A}&=\frac{R_A}{R_B}\\ &=\frac{1}{4}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} L_A&=L_B,\\ I_A\omega_A&=I_B\omega_B\\ \end{aligned} $$ $$ \begin{aligned} \frac{I_A}{I_B}&=\frac{\omega_B}{\omega_A}\\ &=\frac{1}{4}\\ &=0.250 \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \RE_A&=\RE_B,\\ \frac{1}{2}I_A{\omega_A}^2&=\frac{1}{2}I_B{\omega_B}^2\\ \end{aligned} $$ $$ \begin{aligned} \frac{I_A}{I_B}&=\(\frac{\omega_B}{\omega_A}\)^2\\ &=\frac{1}{16}\\ &=6.25\times10^{-2} \end{aligned} $$