You would need ACRES of that shit just to stop them from falling over. And what about a balanced diet. Also, water recyclable isn't 100% efficient, so if you need to feed ACRES of plant life and THOUSANDS of people you're gonna run out after a while. Also it's hydroponics.
Hydropoics - growing plants in nothing but nutritional, recyclable water
I remember the part where they almost died of carbon dioxide poisoning because THE FILTERS AREN'T 100% EFFICIENT. And please don't say oxygen garden. Just, don't. Do you know how much oxygen is consumed by 1000+ people? Daily?
Simply chemical filters. Didn't you ever watch Apollo 13?
Plants eventually die, especially if you're harvesting them so regularly. What about seasons? What are the people going to survive on during the off-periods?
Not really. If there are only 2000-5000 people on a ship the size of a city, you'd only need to dedicate maybe 20% at the most for supplying food.
Okay, I'll accept that one.
As TA said, only a small portion would actually have to rotate.
Politics means there is NO WAY a space-faring vessel will be allowed to store that many potential lethal nuclear weapons on board. But if you DO manage to get them on board, I guess it's plausible.
Remember, this is out of the solar system, not the galaxy. If the majority of the ship were covered in solar panels it could easily hop from star to star - stopping at one star to recharge and then quickly moving to the next. Or as TA said a nuclear reactor.