Why is Olympic slow motion footage sharp with little motion blur? Do the 'broadcast quality' cameras used in the 2016 Olympic Games have higher than normal frame rates? It seems that their slow motion footage is smoother, sharper, and less motion blurred than typical day-to-day productions from local stations.
The MacCAM (used in Tennis back in 2004) used a 1000 fps frame rate and had just enough resolution to capture a tennis ball hitting (or missing) a line with reasonable resolution.  Today, a Phantom Flex 4K can do 1000 fps with UHD or 4K resolution.  Many high-end broadcast cameras can do 120 fps at FullHD or UHD resolution, which is probably what they were using at the Olympics.  That's 4x slow motion for NTSC-land and nearly 5x slow motion for PAL-land.  That is a great frame rate for anything but the fastest sports (badminton, ping pong, etc).

The Panasonic Varicam HS is a broadcast camera that does 240 fps.  I wasn't watching these Olympics closely enough to see whether this was the camera used for the gymnastics event, but wouldn't be surprised if it was.