11-47 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} I&=0.333\ut{kg\cdot m^2}\\ L_i&=3.00\ut{kg\cdot m^2/s}\\ L_f&=0.800\ut{kg\cdot m^2/s}\\ \Delta t&=1.5\ut{s}\\ \end{cases} $$ $$\ab{a}$$ $$\vec \tau_\net=\dyt{\vec L}={\Delta L\over\Delta t},$$ $$ \begin{aligned} \tau&={\Delta L\over\Delta t}\\ &={{L_f-L_i}\over\Delta t}\\ &=-{22\over15}\ut{N\cdot m}\\ &\approx -1.4666666666666666\ut{N\cdot m}\\ &\approx -1.5\ut{N\cdot m}\\ \end{aligned} $$ $$\ab{b}$$ $$L=I\omega,$$ $$\Delta \theta=\frac{1}{2}\br{\omega+\omega_0}t,$$ $$ \begin{aligned} \Delta \theta &={1\over2}\br{{L_f\over I}+{L_i\over I}}t\\ &={L_f+L_i\over2I}t\\ &={95\over111}\ut{rad}\\ &\approx 0.8558558558558559\ut{rad}\\ &\approx 0.86\ut{rad}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} W&=\int \tau \cdot\dd \theta\\ &=\tau \cdot\Delta \theta\\ &=-{22\over15} \cdot {95\over111}\ut{J}\\ &=-{418\over333}\ut{J}\\ &\approx -1.2552552552552552\ut{J}\\ &\approx -1.3\ut{J}\\ \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} P&=\dyt{W}={\Delta W\over \Delta t}\\ &=-{836\over999}\ut{W}\\ &\approx -0.8368368368368369\ut{W}\\ &\approx -0.84\ut{W}\\ \end{aligned} $$