Final answer:
A diver gains angular momentum by pushing against the diving board and controls it by changing body shape, pulling in limbs for faster rotation or extending them to slow down due to conservation of angular momentum.
Step-by-step explanation:
When a diver leaves the diving board, they gain angular momentum primarily by pushing against the diving board (option a). The force they exert on the board through their legs creates a reaction force that initiates rotation, giving them angular momentum. This initial angular momentum is dictated by the push-off. Once in the air, divers manipulate their angular momentum by changing their body shape—pulling in their limbs to increase rotation rate due to the conservation of angular momentum (option b), and extending them to decrease it before water entry (option c).
Pulling in limbs reduces the diver's moment of inertia, causing a faster spin due to the conservation of angular momentum (angular momentum = moment of inertia x angular velocity). Conversely, extending limbs increases moment of inertia, thereby slowing down the spin for a controlled entry into the water. Therefore, all the options a, b, and c contribute to gaining and controlling angular momentum, but it is initiated by the action of pushing against the board.