In the sharp turn in Long Island City, between Queensboro Plaza and 39th Ave., N/W trains enter slow most of the time, but then speed up while the last few cars are still on it. This morning it happened, and I was in the last car. It swayed back and forth so much that I prayed it wouldn't derail, tip over and land on the street below. I imagine that if the last car did capsize it will pull much, if not all, the other cars with it. Such an accident could kill and / or maim hundreds. Has anyone else noticed and given much attention?
Chances of that are about zero. That line has been in service for about 100 years, with higher speeds on that curve than today. The timers do force too low a speed, and so when the train leaves the timer's block it accelerates after braking. This seems to be common, the MTA would rather grind the brakes then accelerate thousands of times per day so that a in the case where a drunk operator, complicit conductor and cover-for-mah-bro supervisors combine as in the Union Square wreck, the train will be moving too slowly for it to matter.
About half the weight of the subway car is in the truck assemblies, so the center of gravity in much lower than you'd think. That said, india gauge would be more stable. BART used that so that their trains could (theoretically) run over the Golden Gate Bridge.
You probably felt that swaying as the train was first leaning to the inside of the turn from going too slowly, then rocked on its springs as the last car cleared at normal speed, relieving the inward tilt but also creating a rocking motion.