While I was watching kids on carousel I've thought about which speed did they have. I've decided that it is easy to find, all you need to do is just measure their revolutions per minute (n) and radius of carousel (R).
With revolutions per minute one can find angular speed - one revolution changes the angle by
radians, thus per minute it is
radians, and per second it is
Radians per second is the angular velocity
. Linear velocity is trivial, 1 radian corresponds to arc with length of radius, thus