Motion in a Vertical Circle

Consider a body of mass 'm' tied to a string and rotated in a vertical circle of radius 'r'. The velocity (speed) of the body keeps changing. It is maximum at the bottom and a minimum at the top.

Let u be the speed of the particle at the bottom

Let v be the speed at some point

By the principle of conservation of energy

Where (h is the vertical height of P above the lowest point)

Let T be the tension in the string.

Sub Topics

Minimum velocity required at the bottom for looping the loop

Minimum velocity required at the bottom for looping the loop

Tension at the highest point is obtained by putting h = 2r in

Tension at the bottom of the circle is obtained by putting h = 0.

Tension at the highest point is given by putting h=2r

T_L - T_H = 6mg