Respuesta :
Given that the mass of each astronaut is m = 74.3 kg
The distance between the two astronauts is d = 13.1 m
The speed of the astronaut is v = 5.65 m/s.
(a) We have to find the angular momentum.
The formula to find angular momentum is
[tex]\begin{gathered} L\text{ = (}\frac{1}{2}d)mv+\text{(}\frac{1}{2}d)mv \\ =\text{dmv} \end{gathered}[/tex]Substituting the values, the angular momentum will be
[tex]\begin{gathered} L=74.3\times13.1\times5.65 \\ =5499.31kgm^2\text{/s} \end{gathered}[/tex](b) We have to find the rotational energy.
The rotational energy can be calculated by the formula
[tex]\begin{gathered} E=\frac{L^2}{2(\frac{2md}{2})} \\ =\frac{L^2}{2md} \end{gathered}[/tex]Substituting the values, the rotational energy will be
[tex]\begin{gathered} E=\frac{(5499.31)^2}{2\times74.3\times13.1} \\ =1.554\times10^4\text{ J} \end{gathered}[/tex](c) We have to find the angular velocity when d'= 5.99 m
The formula to find the new angular velocity is
[tex]\omega=\frac{L}{d^{\prime2}m}[/tex]Substituting the values, the angular velocity will be
[tex]\begin{gathered} \omega=\frac{5499.31}{(5.99)^2\times74.3} \\ =\text{ 2.06 rad/s} \end{gathered}[/tex]