Circular motion velocity components problem

[quark001]

Consider a circular hoop with a radius R and a mass M. Initially the centre of mass of the hoop is spinning, but not moving. Then a object with mass m is thrown at speed v by a spring-loaded gun with an angle of theta anticlockwise from the posive horizontal. Calculate the x and y components of the centre of mass velocity after the object is thrown.

So this looks like a conservation of momentum problem. Since the CM is spinning but not moving, it should have angular momentum but not linear momentum. But how do I calculate it with just R and M? The components of the object's velocity are easy to calculate using theta. But where to from there?

 

[voko]

I do not understand the description. First of all, the CM cannot be spinning. It is a point. Did you mean to say the hoop is spinning?

Secondly, what is the connection between the object, the gun and the hoop? What CM is being used in the final part of the description?