# Law of Motion XVIII

Velocity Relationship at different Points of Vertical Circular Motion:

Let initial and final velocities of the body performing vertical circular motion be v1 and vand the angle made by string with the vertical be θand θ2. Taking lowermost point of vertical circular path as reference level and applying energy conservation,

Vertical Circular Motion of a Body Attached to a Rod

Since rod can never slag hence in the critical situation a body attached to the rod may reach the topmost position A of the vertical circular path with almost zero velocity. In this case its weight mg acts in vertically downward direction and tension of rod acts on the body in the vertically upward direction. Applying net force towards center is equal to centripetal force,
Putting vA = 0 (for critical condition)
mg - TA = 0

or, TA = mg

Critical velocity and Tension at the lower most point
Taking B as reference level of gravitational potential energy and applying energy conservation

Putting, vA= 0(for critical condition)

This is the minimum possible velocity at the lower most point for vertical circular motion known as critical velocity at point B.
vB(Critical) = √4rg

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