Rotational Power

Linear power is force times velocity. Rotational power is the exact same idea rewritten for spin: torque times angular velocity, P = tau x omega. Torque is the rotational stand-in for force, and angular velocity (omega, in rad/s) is the rotational stand-in for speed. A motor spinning fast while pushing with a lot of torque delivers a lot of power, same as a car pushing hard while moving fast delivers a lot of power on the highway.

This is why an engine's power rating always comes with a specific rpm attached. Power is not fixed to a motor the way torque sometimes is near-fixed by its design. As angular velocity changes, the torque needed to produce a given power changes too, so a power number alone means nothing without knowing the spin rate it was measured at.

This connects directly to gearboxes and anything with rotating shafts. If a gearbox keeps power roughly constant (real gearboxes lose a little to friction and heat, but assume none here) while cutting angular velocity down, torque has to go up to compensate, since P = tau x omega means the two trade off directly. That is the whole reason low gears exist: they sacrifice speed to multiply torque for climbing hills or hauling loads, while high gears do the opposite, trading torque for speed once momentum is already built up.