We measure rotational power output with dynamometers. They vary in form but the general idea is to accelerate a mass with known characteristics over a set length of time.
For example, if we have a tire in contact with a steel drum (and we know the drum’s rotational inertia – it’s resistance to accelerating) we can measure the change in spinning speed of the drum over a period of time. Since w can calculate how much energy it takes to speed up the drum that much and since we measured the time, we can calculate power (energy/time)! The math for ths method had been around longer than motor vehicles.
Other dynamometers test engine (or shaft power) by accelerating a fluid (like water or oil) with a pump.
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