Fluttering
If one releases a stationary piece of paper in air, then unlike a coin, it does not typically maintain the same orientation as it falls. Small pieces of paper spin in a repetitive way; but larger pieces of paper tend to flutter in a seemingly random way (as discussed, among others, by James Clerk Maxwell in 1853). A similar phenomenon can be seen if one drops a coin in water. I suspect that in these cases the randomness that occurs has an intrinsic origin, rather than being the result of sensitive dependence on initial conditions.