In reply to Baz P:
Yes. If power is Force x Distance / Time then to achieve the same power holding Force the same his foot needs to cover a fixed (circumferential) distance in a given time. With the longer circumference of a longer crank he would do fewer revolutions per unit time.
I think the use of shorter cranks muddies the water when it comes to the cadence debate. For a given crank length a higher cadence means lower force which (up to some value) seems to reduce fatigue. Shorter cranks lend themselves to a higher cadence, but that does not come with a reduction in force (as we have seen above), so it is not clear whether that reduces fatigue.
Instead I suspect there is some bio-mechanical reason for the (purported) advantage of short cranks. Reduction in knee flex and associated injury has been suggested, or that the leg muscles work in a more efficient part of their range of motion.