10-54 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} A : 0\lt t\lt 20\ut{s}\\ B : 20\ut{s}\lt t\\ \end{cases} $$ $$ \begin{cases} \omega_0&=0\\ \omega_2&=5.0\ut{rad/s}\\ \alpha_A&=\Cons\\ \alpha_B&=0\\ \theta_0&=0\\ \end{cases} $$ $$ \begin{cases} \omega&=\omega_0+\alpha t\\ \Delta \theta&=\omega_0t+\frac{1}{2}\alpha t^2\\ \end{cases} $$ $$ \begin{cases} \omega_2&=\omega_0+\alpha t_2\\ \Delta \theta_{0\rarr20}&=\omega_0t_{20}+\frac{1}{2}\alpha {t_{20}}^2\\ \end{cases} $$ $$ \begin{cases} \omega_2&=\alpha t_2\\ \theta_{20}&=\frac{1}{2}\alpha {t_{20}}^2\\ \end{cases} $$ $$ \begin{aligned} \theta_{20}&=\frac{{t_{20}}^2 }{2 t_2}\omega_2\\ &=500\ut{rad}\taag1\\ \end{aligned} $$ $$ \begin{cases} \omega_2&=\omega_0+\alpha t_{0\rarr2}\\ \omega_{20}&=\omega_0+\alpha t_{0\rarr20}\\ \end{cases} $$ $$ \begin{aligned} \frac{\omega_{20}}{\omega_2}&=\frac{t_{0\rarr20}}{t_{0\rarr2}}\\ \omega_{20}&=\frac{t_{0\rarr20}}{t_{0\rarr2}}\omega_2\\ \end{aligned} $$ $$ \begin{aligned} \Delta \theta_{20\rarr50}&=\omega_{20}t_{20\rarr50}\\ &=\frac{t_{0\rarr20}}{t_{0\rarr2}}\omega_2t_{20\rarr50}\\ &=1500\ut{rad}\taag2\\ \end{aligned} $$ $$ \begin{aligned} \Sigma \theta&=\theta_{20}+\Delta \theta_{20\rarr50}\\ &=2000\ut{rad}\\ &=2.0\times10^3\ut{rad}\\ \end{aligned} $$