I came across this pretty interesting 1950s USN Training film on how the mechanisms for the Mark 1 Fire Control Computer and Mark 37 Gun Fire Control system works. It's basically a basics of how an analogue computer could be build to perform mathematical operations. These videos are more for the historian/engineer/mathematician nerds that lurks about these parts rather than for people looking for explosions. Enjoy!
Basic Mechanisms In Fire Control Computers: Shafts, Gears, Cams... 1953 US Navy Training Film Part 1
Basic Mechanisms In Fire Control Computers: Solvers, Integrators... 1953 US Navy Training Film Part 2
I guess for those of you who are looking for some explosions here's a training film of how the 3x16" gun turret on the Iowa works.
Battleship Guns: "16 Inch Gun & Turret" 1955 US Navy Training Film for Iowa Class Battleships