## Saturday, January 9, 2016

### Minimum velocity at the top of vertical circular Motion

For the body to move in vertical circular motion, we shall give minimum velocity at different points of the motion. Here in the post, we are going to identify the minimum required velocity at the top of the vertical circular motion.

For any body to be in vertical circular motion, there need to be centripetal  force.  Centripetal force is the effective existing force acting towards the center of vertical circular motion.

Let us consider a body of mass m is revolving in the vertical circular motion of radius r.  There is a string of length r attached to the mass to rotate the body in the vertical circular motion. Weight of the body always acts in the downward direction and it is due to acceleration due to gravity of the earth. The string becomes tight due to this and it generates tension in the string. Tension is  a force which makes the strings tight. Tension always acts away from the body and towards the point of suspension.

The effective force acting towards the center at the top of the vertical circular motion is the sum of tension and weight. Hence the tension in the string at the top is the difference between centripetal force and weight of the body.

For the body to continue vertical circular motion, at the top gravitational force is helping. Even if the tension is not there in the string, gravitational force provides the necessary centripetal force to rotatory body in vertical circular motion. Thus for the minimum velocity at the top of the vertical circular motion, tension can be equated to zero.

By simplifying it further as shown in the video lesson below, we can get the velocity of the vertical motion as shown below.

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