For example, imagine an object of a certain mass which is attached to a rope and is dangling in the air. The rope needs to have a certain tension to be able to hold the object up, that is, negate the effects of gravity pulling it down. I'm wondering, if you took the other end of the rope and started pulling it upwards, would the tension need to be higher to still keep the object from falling? For example if a helicopter is carrying an object attached to a rope under it, would the tension of the rope need to be different for when the helicopter is hovering in the air and when it's flying upwards?
I'm wondering this because it feels like that should be the case, especially when I think about how swinging the rope rapidly in circles might make the object detach and fly off, even if it would've stayed on had the rope not been in motion.