Why is Olympic slow motion footage sharp with little motion blur?
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.