10-28 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} r&=12\ut{m}\\ \theta&=0.20t^2\\ t&=5.0\ut{s}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \omega&=\dyt{\theta}\\ &=\dt\(0.20t^2\)\\ &=\frac{2}{5}t\\ \end{aligned} $$ $$ \omega(5)=2.0\ut{rad/s} $$ $$\ab{b}$$ $$ \begin{aligned} v&=r\omega\\ &=r\(\frac{2}{5}t\)\\ &=\frac{24}{5}t\\ \end{aligned} $$ $$ v(5)=24\ut{m/s} $$ $$\ab{c}$$ $$ \begin{aligned} a_t&=r\alpha\\ &=r\cdot\dyt{\omega}\\ &=r\cdot\dt\(\frac{2}{5}t\)\\ &=\frac{2r}{5}\\ &=\frac{24}{5}\ut{m/s^2}\\ &=4.8\ut{m/s^2}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} a_r&=r\omega^2\\ &=r\cdot\(\frac{2}{5}t\)^2\\ &=\frac{48}{25}t^2\\ \end{aligned} $$ $$a_r(5)=48\ut{m/s^2}$$