11-12 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} R&=\frac{75.0}{2}\ut{cm}=\frac{3}{8}\ut{m}\\ v_0&=105\ut{km/h}=\frac{175}{6}\ut{m/s}\\ \Delta \theta &= 30\ut{rev}=60\pi\ut{rad}\\ v_1&=0\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \omega&=\frac{v}{R}\\ &=\frac{700}{9}\ut{rad/s}\\ &\approx 77.77777777777777\ut{rad/s}\\ &\approx 77.8\ut{rad/s}\\ \end{aligned} $$ $$\ab{b}$$ $$2\alpha \Delta \theta=\omega^2-{\omega_0}^2,$$ $$ \begin{aligned} \alpha&=\frac{\omega^2-{\omega_0}^2}{2\Delta \theta}\\ &=\frac{12250}{243\pi}\ut{rad/s^2}\\ &\approx 16.046486031898915\ut{rad/s^2}\\ &\approx 16.0\ut{rad/s^2}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} S&=2\pi R \cdot N\\ &=\frac{45\pi}{2}\ut{m}\\ &\approx 70.68583470577035\ut{m}\\ &\approx 70.7\ut{m}\\ \end{aligned} $$