These are essentially two-phase induction motors with permanent magnets that retard rotor speed, so their speed is quite accurately proportional to wattage of the power passing through the meter. The rotor is an aluminum-alloy disc, and currents induced into it react with the field from the stator. One phase of the stator is a coil with many turns and a high inductance, which causes its magnetic field to lag almost 90 degrees with respect to the applied (line/mains) voltage. The other phase of the stator is a pair of coils with very few turns of heavy-gauge wire, hence quite-low inductance. These coils are in series with the load.
The core structure, seen face-on, is akin to a cartoon mouth with one tooth above and two below. Surrounding the poles ("teeth") is the common flux return path. The upper pole (high-inductance winding) is centered, and the lower ones equidistant. Because the lower coils are wound in opposition, the three poles cooperate to create a "sidewise" traveling flux. The disc is between the upper and lower poles, but with its shaft definitely in front of the field, so the tangential flux movement makes it rotate.
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