revolution

The revolution is the angle unit machines count in, because so much of machinery is organised around the complete turn: a gear tooth engages once per revolution, a positive-displacement pump moves a fixed volume per revolution, and a rotary encoder is specified in counts per revolution. Odometers, energy-meter discs and engine tachometers all count whole turns rather than radians, and nameplate speeds arrive as revolutions per minute.

A four-stroke engine gives the unit a twist worth remembering: each cylinder fires once every two revolutions, because the cycle needs four strokes and each revolution supplies only two. A four-cylinder engine at 3,000 rpm therefore produces 100 firing pulses per second, and that 100 Hz pulse train is the drone you hear at motorway speed. For calculation, though, the revolution has to leave the stage early. The rotational solvers on this site, like every dynamics formula, work in radians, so a count in revolutions is multiplied by $2\pi$ on the way in, and the caution above about rpm's two readings is the same factor of $2\pi$ wearing different clothes. Counting turns is for people and meters; the mathematics wants the angle.