1. The problem statement, all variables and given/known data Space Station A space station has the form of a hoop of radius R, with mass M. Initially its center of mass is not moving, but it is spinning with angular speed ω0. Then a small package of mass m is thrown by a spring-loaded gun toward a nearby spacecraft as shown; the package has a speed v after launch. (a) Calculate the center-of-mass velocity of the space station (vx and vy) and its rotational speed ω after launch. Do not worry about italics. For example, if a variable R is used in the question, just type R. To specify the angle θ simply use the word theta. Likewise, for ω0 use the word omega0. vx = vy = ω = 2. Relevant equations vx = (m/M)(-v)cos(theta) vy = (m/M)(-v)sin(theta) 3. The attempt at a solution I know that I must use the angular momentum principle, and that the component is out of the page (+z) I*ωi + R*m*v1(=0)*cos(theta) = I*ωf + R*m*v2*cos(theta) I = MR^2 so ωf = ωi - R*m*v2*cos(theta)/(MR^2) Can somebody please let me know where I am going wrong in my derivation of ωf because apparently this is wrong, yet my book does not have any solutions.