Two small balls A and B , each with mass m , are rigidly attached to the ends of a light rod of length L . Over a frictionless horizontal surface, the system translates with a velocity v₀ directed perpendicular to the rod. A stationary particle P of mass m on the surface sticks to ball A as the ball collides with it. Compute the angular speed of the system about its centre of mass C following the collision.

Step-by-step solution

Let the new centre of mass of the system after the collision be C' . After the stationary particle P sticks to ball A , the mass at A becomes m + m = 2m , while the mass at B remains m . The distance of the new centre of mass C' from A is: x = m L + 2m 0 3m = L 3 The distance of C' from B is L - L 3 = 2L 3 . The moment of inertia of the system about C' after the collision is: I = 2m ( L 3 )^2 + m ( 2L 3 )^2 I = 2mL^2 9 + 4mL^2 9 = 2mL^2 3 We apply the principle of conservation of angular momentum about C' just befo