Circular brakes
Like linear eddy current brakes, circular brakes also have one static part and one moving part. They come in two main kinds, according to whether the electromagnet moves or stays still. The simplest ones look like traditional brakes, only with a static electromagnet that applies magnetism and creates eddy currents in a rotating metal disc (instead of simple pressure and friction) that moves through it. (The Shinkansen brakes work like this.) In the other design, the electromagnets move instead: there's a series of electromagnet coils mounted on an outer wheel that spins around (and applies magnetism to) a fixed, central shaft. (Telma frictionless "retarder" brakes, used on many trucks, buses, and coaches, work this way.)
How do these things work in practice? Suppose you have a high-speed factory machine that you want to stop without friction. You could mount a metal wheel on one end of the drive shaft and sit it between some electromagnets. Whenever you wanted to stop the machine, you'd just switch on the electromagnets to create eddy currents in the metal wheel that bring it quickly to a halt. Alternatively, you could mount the electromagnet coils on the rotating shaft and have them spin around or inside stationary pieces of metal.
With a linear brake, the heat generated by the eddy currents can be dissipated relatively easily: it's easy to see how it would disappear fairly quickly in a brake operating outdoors over a relatively long section of train track. Getting rid of heat is more of an issue with circular brakes, where the eddy currents are constantly circulating in the same piece of metal. For this reason, circular eddy current brakes need some sort of cooling system. Air-cooled brakes have metal meshes, open to the air, which use fan blades to pull cold air through them. Liquid-cooled brakes use cooling fluids to remove heat instead.