# Tension at topmost point of a vertical circle

I read that for a body to move in a vertical circle, the minimum tension needed is 0 at the topmost point. Can someone explain to me what it means to have positive or negative tension on top. I'm not able to visualise it.

First you need to think what is tension. Tension is a strain that is created in the rope (or string) when a force tries to elongate the rope. It means if no force to elongate, then no tension.

Now taking the example you asked about. If there is a tension in the string at topmost point then it will revolve because that tension is the centripetal force which causes it to make the circular motion.

What if the tension is $0$ at the topmost point? No problem. The linear speed (which acts perpendicular to the centripetal force i.e. tension in this case) will keep it in motion.

What is positive tension? It's the tension in the string that comes into play when, say, you try to elongate the rope.

What is negative tension? It's when you try to compress the rope. But wait, you can't do it because if you do it then it will bend but won't compress. So the tension in the string will be zero. You may get it in some numerical problems because it tells how much force we have applied till the tension became zero from positive.

• Thank you. This was what I was looking for. Say while solving a question, I happen to get tension negative at the topmost point does that mean the string became slack before reaching the top most point? Dec 9, 2015 at 10:21
• @user93868 exactly... Dec 9, 2015 at 13:58

This is not a universal principle; to be able to speak of tension, you must have an object that attaches the moving body to some other object. Take a yo-yo as the moving body, which is attached by a string to your finger. When you spin it to a looping, and you don't have enough tension in the string, it will fall down before it reaches the top, because the string loses its tension, in other words, it collapses. You can't have negative tension in a string, but you can have it in a spoke: Intuitively, it just means that if you replaced the spoke with a string, it would collapse. If you have exactly 0 tension exactly at the top, then it's just enough for the yo-yo to keep doing the looping.