## Friday, January 8, 2016

### Tension in String in Vertical Circular Motion

A body attached to a string can be executing vertical circular motion. At each point of motion, it will have different tensions in the string. For any body to be in circular motion there shall be centripetal force acting on it. Centripetal force is not a out side force. The very existing  effective force in circular motion that is acting towards the center is called centripetal force. Tension is a force generated in the wires and strings when a force is applied on them. Tension generate tightness in the wire or string.

Let us consider a body of mass m  attached to the string of length r and is rotated in circular motion against gravitational force in vertical circular motion.

At any point, weight of the body always acts in the downward direction.It is due to gravitational force and it acts always towards the center of the earth. Hence gravitational force always acts in the downward direction.

Tension always try to keep the string tight and always acts towards the point of suspension  or point of center from where the body is moving. Tension also acts away from the body in the string so that it can keep the string tight.

We can identify centripetal force at each instant as the resultant force acting on the body towards the center.When the body is at the bottom of the vertical circular motion, weight is acting in the downward direction and tension is acting towards the center and away from weight. So effective centripetal force is difference between tension and weight.

Let the body is at a particular angle to the vertical that is to the gravitational force. We can resolve the weight into components as it is a vector quantity. It can be found that the horizontal component is against the tension and hence we can write effective force as the centripetal force shown in the video below.

If the string is in the horizontal position, weight has no component acting towards the center and hence it won't contribute for the centripetal force. The only force acting towards the center is tension and it acts like centripetal force.

This is shown in the video lecture below in detailed presentation.

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