# 136 Ball tied to String in Circular Motion

The tension in the string is changing during the circular motion. Why?

Firstly, note that the vertical circular motion of a ball swung on a string is not uniform circular motion where the speed is constant.Gravity causes the ball’s speed to be fastest at the bottom and slowest at the top. (vB>vT) As such the required centripetal force is maximum at the top of the circle, and minimum at the bottom of the circle. (mv2/r)

There are thus two reasons why the string is most taut at the bottom.

1. The required centripetal force at the bottom is maximum.(mvB2/r)
2. Weight of the ball is in opposite direction to the centripetal direction. The tension in the string must overcome the weight before contributing to the required centripetal force. (T = mvB2/r + mg)

There are also two reasons why the string is least taut at the top.

1. The required centripetal force at the top is minimum. (mvT2/r)
2. Weight of the ball is in the centripetal direction. The weight assists the string to provide the required centripetal force. (T = mvT2/r  mg)

In fact, if the ball is swung too slowly, gravity may pull the ball down so quickly that the string becomes slack and the ball becomes a projectile motion instead. The minimum launch speed in order to complete the circular motion successfully is presented in this xmtutor video.