focal length vs shutter speed vs fps
Shutter speed and focal length are completely independent parameters, focal length determines angle of view (how much scenery you get in your shot). Shutter speed determines how long each part of the image sensor is exposed for, and therefore it determines the brightness of the image, and how much blur is caused by moving objects.

The quantity that most commonly relates the two is camera shake. It is often advised that to avoid camera shake the shutter speed must be 1/focal-length. This is presumably where you've gotten this equivalence from. The rule is a guideline only and depends on your technique and degree of enlargement in the final image. A better guideline is shutter-speed = 3/focal-length



FPS, or frames per second is the number of images per second recorded by your camera. It is related to shutter speed in that shutter-speed + latency &lt; 1/FPS. If each frame takes more than a 60th of a second to expose, then you are not going to be able to cram more than 60 exposures in a second! There is a nonzero amount of time required to recock the shutter mechanism (if necessary) and readout and store the image, which is the latency. In stills cameras not designed for continuous readout the latency can increase as buffers become full, causing the maximum obtainable FPS to drop.

The formula shutter speed = 1/(2*FPS) relates to a shutter angle of 180 degrees, which is a concept from film cine cameras whereby the film can only be exposed for a maximum of half the intra-frame time, because of the rotating shutter. This rule is still obeyed by digital filmmakers to ensure "cinema like" motion to the image, compared to if shutter speed = 1/FPS which gives more fluid "TV like" motion.