Answer:
The question is incomplete however this kind of questions about determinate the angular speed and taking a reference of days rotating the first star.
w=0.11312 rad/s
Explanation:
The situation is about a two star the question is incomplete, miss the time rotate one star so we assume the first star rotated once in 30 days so:
Angular momentum
[tex]P_{m}=I*w[/tex]
The inertia
[tex]I=\frac{3}{5}*m*r^2[/tex]
The momentum must be conserved so
[tex]P_{m1}=P_{m2}[/tex]
[tex]I_{1}*w_{1}=I_{2}*w_{2}[/tex]
[tex]\frac{2}{5}*m*r_{1}^2*w_{1}=\frac{2}{5}*m*r_{2}^2*w_{2}[/tex]
notice don't have to know the mass or use the density however at the end can determinate
[tex]w_{2}=\frac{r_{1}*w_{1}}{r_{2}}[/tex]
Time can determinate the frequency so determinate angular speed of the first star
[tex]w_{1}=2\pi*f_{1}[/tex]
[tex]t_{1}=30days*\frac{24hr}{1day}*\frac{60minute}{1hr}*\frac{60s}{1minute}=2592000s[/tex]
[tex]f_{1}=\frac{1}{t_{1}}=\frac{1}{2592000}=3.858x10^-7Hz[/tex]
[tex]w_{1}=2.424x10^{-6}\frac{rad}{s}[/tex]
[tex]w_{2}=\frac{7.0x10^8m}{15x10^3m}*2592000[/tex]
[tex]w_{2}=0.11312 rad/s[/tex]
