Let's say I have a ball attached to a string and I'm spinning it above my head. If it's going fast enough, it doesn't fall. I know there's centripetal acceleration that's causing the ball to stay in a circle but this doesn't have to do with the force of gravity from what I understand. Shouldn't the object still be falling due to the force of gravity?
[Physics] Why doesn’t a spinning object in the air fall
centripetal-forceforceshomework-and-exercisesnewtonian-mechanics
Best Answer
The string is at a slight angle to horizontal $\theta$. It is not exactly horizontal. The slight angle is such that the tension in the string exactly counteracts gravity, $T\sin(\theta)=m g$. So, there is actually a force acting upwards that counteracts gravity, and it is supplied by the string.
You're right that if $\theta=0$ exactly, there would be a problem and the object would necessarily fall a bit.