Why doesn't a particle in uniform circular motion fall into the centre? If a object is in uniform circular motion, I know there is a acceleration directed radially inward. If that's the case, shouldn't there be a velocity radially inwards at some time. If that's true. Why does it not fall in that direction? know that i am a idiot. Please help me see how it works.
 A: No idiots here; this is a perfectly valid question and one of many examples of very normal situations that just don't fit our intuition at first glance. 
Think of a ball on a string. 


*

*Imagine that the ball is still (not moving). Pull the string and it accelerates towards the centre. The resulting acceleration is only towards the centre. 

*Now imagine that the ball is moving tangentially to an orbit-path. Pull the string and it accelerates towards the centre. The ball will now in the next instant move a little bit inwards but also still a little bit to the side because of the initial tangential speed. The combination (resulting velocity) does not point towards the centre but also not tangentially anymore. It rather points around and starts an orbiting path. 


The point is that the ball is trying to fall inwards to the centre the whole time, but it "misses" and falls "around" it instead. 
A: Let the particle be a ball swung around and is tied with a string. Now everyone knows that acceleration on ball is inwards. When you are asking this question, you must be completely clear about what is the meaning of "falling". Indeed the ball is falling everytime.

Here you may see the particle falling, literally.

You may don't see the particle falling but it is always falling. The only difference is that in circular motion, the direction of acceleration changes every moment and thus it keeps on falling in different directions, which later on makes it move in circular motion.
Thus falling can be termed as a motion under the virtue of any Force, of course in the same direction of the Force. So falling is similar to any other motion.
