Simple example: put your frictionless spherical cow on a spinny plate. Make it a very small cow; it's only there to have a point of rotation. Why frictionless? You don't want its butt to catch fire. Why spherical? It'll need to maximize volume dedicated to arm muscles; see below.
Have the cow hold two ropes, each leading to a full-sized cow 10m away. Apply force to those cows (blow on them, or magnetize them and do a solenoid thing, or just make them very gassy cows and orient their spherical butts in opposite directions). Get them spinning at 1Hz. (This is very fast; remember the diameter is 20m.) Now have the middle cow pull the ropes, shortening them to 10cm. It's now spinning at 1Khz. 10mm gives 1Mhz. Conservation of angular momentum, baby.
Do this in a vacuum in microgravity, and you don't need the center cow.
Sure, if you're doing this at a bovine scale, the tension is ridiculously large. What makes it infeasible at a small scale?