Whirlpool ADG 7550 Spray Motor

My dishwasher has stopped spraying water altogether as far as I can tell, but it does fill with water, heat it and drain it out again, so the drain pump and heater element are working. I’m guessing the problem is the spray pump, which has been making some odd noises lately but now just seems to hum. So I took it out last night, removed the impeller cap and applied power to the motor on my workbench. I was surprised that it did run, but it was quite slow, about 200rpm (very approximately) and wobbly.

I see from the service manual that there is a 4µF capacitor for this motor. I didn’t see it, but then again, I wasn’t looking for it. The service manual does not list a part number for the capacitor.

So my question, at last: does it sound like the motor is faulty, or maybe the capacitor is? Assuming the capacitor is much cheaper than a new motor, can it be replaced separately? Thanks for reading.