Binary Stars: Moment of Inertia & Angular Momentum

[lucifer]

two stars, A and B, are in circular orbit of radii r1 and r2, respectively, about their common center of mass. each star has the same period of revolution T.

Determine expressions for the following two quantities in terms of the stars' masses, radii and T.

1- the moment of inertia of the two star system about it's center of mass
2- the angular momentum of the system about the center of mass

for the moi, i highly doubt it but... would it just be m1r1^2 + m2r2^2 ?

and then to find the angular momentum i can just multiply the I i got before with 2pi/T... ?

thanks. :-)

 

[Parth Dave]

Consider the centre of mass of the system to be the rotational axis. The moment of inertia is simply the sum of the individual moments. Each moment is given as mr^2. What does that make the moment of inertia?

 

[Galileo]

The answers look fine to me.
Be sure to convince yourself that the planets are rotating in the same direction (both clockwise or both counterclockwise), so you can add the angular momenta of the two instead of subtracting them.