Wednesday, January 6, 2016

Velocity at any point in Vertical Circular Motion

If a body  is revolving around a fixed axis, then it is called rotational motion and the axis is called axis or rotation. Different particles of the body rotates about the axis of rotation but  particles of the body on the axis of rotation remains in the state of rest. If the body is rotating against the acceleration due to gravity, then it is called vertical circular motion.

Let us consider a particles of mass m rotating in vertical circular motion with a thread of length r revolving in a vertical circle. We can consider any two points in the journey and we can apply law of conservation of energy at that two points. The total mechanical energy at that two points is equal. Mechanical energy is the sum of potential energy and kinetic energy.

We can consider the bottom of vertical circular motion as a the reference point and from that point we can measure the potential energy. At the reference point, potential energy is treated as zero. Let us assume that we have given some known velocity at a given point and we need to measure the velocity at any other point in terms of the initial velocity of the reference point.

As the body moves from reference point to a new position, it will gain some potential energy and automatically  its kinetic energy decreases. With reference to the ground level point, the new point is at a certain height and hence it will have corresponding potential energy. If the height of the body is not given from reference point, we can express the height of the body in terms of the angle made by the body with respect to axis of rotation.

By substituting the value of the height in the equation of velocity, we can find the velocity of the body at any point in terms of inclination of the body.

If the body is at the horizontal position, the angle is 90 degree and by substituting this value in the equation of velocity at any point of the vertical circular motion, we can find the  velocity even at the horizontal as shown in the video lesson presented below.

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