Collision of 2 Stars: Calculating Angular Velocity & Momentum

[Gogsey]

So the question is basically,

A stationary spherical star sits at the origin, and has mass 8M and radius 2R. Another sphere of mass M and radius R has a velocity and is coming toward the larger mass. We are to neglect gravitational effect until the 2 masses come into contact. What happens is that the edge of each mass comes into contact and the combine the make an even larger star. Both maases are to be treated as spherical liquid state objects with uniform density before and after the collision. When they come into contact they merge instantly. We are to calculate the angular velocity and angular momentum of the final star.

So the moment of inertia of a sphere is 2/5 MR^2.

Trouble is that is the larger star spinning on its axis? If it is then angular momentum should be 64/5 MR^2, if we take the smaller sphere to be the unit sphere. If not, then its angualr momentum should be zero, right?

Also, I'm assuming if gravity has no effect, then the path should be a straight line, right?

It seems like bfore the collision is linear momentum, and after the collision is angular momentum. How can you equate linear and angular momentum?

 

[AEM]

Was the smaller star originally traveling along a line connecting the centers, or was it traveling along a line that was offset, so there is an impact parameter (the perpendicular distance between the center of the largest star and the approach path of the smaller star when the smaller star was far away.)

Remember angular momentum has to be conserved.