Let us consider a string of length r. Let a particle of mass m be attached to the string so that it is rotating in vertical circular motion. Hence, r is the radius of the circle.

Let P represents an arbitrary position of the particle, where the string makes an angle θ with the vertical. If v be the velocity of the particle at this position then considering forces on the particle we can write

• Centripetal force mv²/r acts pointing towards the centre of the circle
• The tension T in the string acting inwards
• The weight mg of the mass m acts in the downward direction

For a point P anywhere in the string, making an angle θ with the vertical, the velocity could be got by equating

mv²/ r = T – mg cos θ

Another important consideration in vertical circular motion is that the total mechanical energy is always conserved. At the highest point in the circle, the potential energy is maximum and at the lowest point in the circle, kinetic energy is maximum. The sum of the PE and KE is always the same throughout the circle.