# Why doesn't a particle in uniform circular motion fall into the centre? [duplicate]

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.

• Possible duplicate of Uniform Circular Motion – John Rennie Dec 26 '15 at 9:47
• Hi Subhranil. The question I've linked has a very misleading title but it is actually the same question as yours because it asks: Why does the object not go inward, into the circle if the acceleration is inward?. – John Rennie Dec 26 '15 at 9:49
• – Qmechanic Dec 26 '15 at 10:34
• The reason the object is in uniform circular motion is because of the inward acceleration component. Try and imagine why the satellite doesn't crash on earth and why while taking a turn in the car your car doesn't move towards the point of turn? – Vinay5forPrime Dec 26 '15 at 12:17
• To be sure, if the particle is in uniform circular motion then, by definition, it is moving in a circle with constant speed, i.e., there is zero radial velocity. Are you asking if uniform circular motion is possible? – Alfred Centauri Dec 26 '15 at 14:08

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.

• Thank u so much for ur answer. But doesn't the velocity that is trying to take it in (towards the centre) increase with time ? ( for it is accelerating ) so the resultant must also change in magnitude. So ? Can u help me clarifying this ? – Subhranil Sinha Dec 26 '15 at 9:43
• Sure, you are right that when the string is pulled, a velocity component towards the centre (that is, along the acceleration which is towards the centre) starts to be created. But in the next instant, where the velocity is turned a little bit (the resulting velocity mentioned in the question), remember that the acceleration also turns since the ball has moved to another position. The acceleration therefore pulls perpendicularly to the new velocity vector. And the whole thing repeats itself. – Steeven Dec 26 '15 at 9:54

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.