Linear and Angular Accel

[carrotstien]

There is a thin ring of mass M radius R. At each direction, north, south, east, and west, you have a rocket that pushes with a constant F newtons. Each rocket push vector is Nx,Ny, Ex,Ey, Sx,Sy, and Wx,Wy.

The ring's center of mass is moving at V so that Vx and Vy are the components of velocity in the x and y direction respectively.

The ring is also spinning with an angular velocity of Z radians per second clockwise.

The rockets are much lighter than the ring so that they don't really affect any calculation due to their relatively small mass.

What are the linear and angular accelerations of the ring?