Two identical pucks, each of inertia m, are connected to a rod of length 2r and negligible

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Question:

Two identical pucks, each of inertia m, are connected to a rod of length 2r and negligible inertia that is free to rotate about its center (it is pivoted at the center). A third puck of inertia m/2
strikes one of the connected pucks perpendicular to the rod with a speed v _i. Assume the collision is elastic.
(a) Draw a diagram of the situation, clearly labeling the direction of vi and what direction the connected pucks will rotate.
(b) Is the total momentum of the system (the three pucks and the rod) conserved throughout the interaction? Why? Is the system isolated, or can you identify an external force acting on it?
(c) Is the total kinetic energy of the system conserved? Why? If you found an external force in part (b), explain why it does or does not do work on the system.
(d) Is the total angular momentum of the system conserved? Why? If you found an external force in part (b), explain why it does or does not exert a torque on the system.
(e) Write down an expression for the moment of inertia (rotational inertia) of the system formed by the connected pucks.
(f) Based on all of the above, write down equations expressing the conservation of the two quantities that are in fact conserved. These equations should involve only the given data (masses, length of rod); the initial and final velocities, v _i and v _f, of the free puck; and ω, the angular speed of the connected pucks after the collision. (Assume the final velocity of the free puck lies along the same line as its initial velocity, that is, it does not bounce off at some random angle.)