I recently received a foldable bike basket which attaches to my back rack as a gift, which I am really excited about - it will make my commute a lot easier. However, I am not sure which side of the bike to attach it to. It seems like putting it on the right side makes sense but when I add groceries or other things to carry it will put the balance out of whack, since the gearing is also on that side. I suppose this is going to happen either way with a single bike basket. Having two would allow me to keep weight and balance even. But with this in mind, should I specifically place the basket on the left side to keep weight more even?
I'm speaking from personal experience here. Looking at the bicycle from the back. The drive train is on the right side, and when you use the kickstand it leans to the left.
When I commute to work, I tend to put my messenger bag with rear rack attachments on the left side. Mostly because the bike is already leaning that way. Once, when I was getting ready to leave work. I placed the bag on the right, and proceed to begin to tie my pants so they wouldn't get caught in the chain. The whole bike, bag and all, fell right on top of me. The incline of that particular part of the parking lot and the weight of the bag were enough to throw the whole bike of balance and rendered the kickstand useless.
Since then, I've always put my bag on the left side. The idea of my bike falling on the right side and bending or breaking a derailleur just freaks me out since I've yet to learn how to fix them or adjust them.
Both sides will be essentially equally safe.
The difference in weight between the sides is quite small. Looking on Weight Weenies a cassette is about 300 grams, a crankset is lets say 800 grams, a chain is another 250 grams, and lets say a freehub is an 400 grams. This means the right side has about 2 kg more stuff on it than the left for the drivetrain stuff (which is quite a small weight relative to the total weight of the bike and rider).
This isn't going to make a difference either way you put the basket on the bike (since the unbalancing weight will be enough to unbalance the bike on either side). If you are loading to the point that the bike is going to be unbalanced with the basket, get two baskets and fill them up equally.
That being said, I'd probably put the basket on the side opposite you normally get on the bike in case my foot hits it while getting on. But this is purely personal preference.
The most practical mechanical effect I can think of is that placing a bag on the right side may protect the rear derailleur in the event of a tip-over. On the other hand, it can sometimes be tricky to install bags on the right because they can interfere with the loop of derailleur cable.
The only other mechanical consideration that hasn't been mentioned is that the rear wheel is built asymetrically, with spokes on the left angled out further than spokes on the right. This may make it slightly safer to have the extra load on the right (because the sideways force from bumps will tend to tension the left side spokes rather than de-tension them.) I think that you will have to carry enough load for the bicycle to become unpleasantly unbalanced before this consideration would have any real effect though.
A more practical consideration is riding in traffic. A large pannier sticking out to the left (in a country that drives on the right) is a great place for reflectors, and may encourage passing cars to give more room. I usually place panniers on the left for that reason.