For the Explain XKCD article:

The typical Ferris wheel has a diameter of about 200 feet and usually takes around 10 minutes per full rotation. The apparent ratio between the connected wheels in the comic is approximately 12.5:1, meaning the motion is significantly sped up as it’s transferred. The second Ferris wheel, driven by the first, could spin at around 1.3 rpm, with passengers moving at 9 mph (14 km/h), which is faster than usual but not inherently dangerous. However, when this motion is further transferred to the third Ferris wheel, it could spin at 16 rpm, with passengers traveling at over 110 mph (180 km/h), subjecting them to 8 Gs of force—conditions that would be hazardous.