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?