# Tension in vertical circular motion

In vertical circular motion we conserve energy for calculating velocities at a point (if initial velocity given). But, energy can only be conserved when forces are conservative. Tension is not a conservative force. Does it not affect the particles velocity? Is the tension's role only to provide centripetal acceleration?

• What makes you say that tension isn't conservative? – Will Cross Nov 23 '13 at 22:52

For example, with the right starting conditions, the velocity of the mass as it "goes over the top" will be $\sqrt{Rg}$, and gravity will supply all the centripetal force needed; at that moment, the tension would be zero.
$$W = F \cdot s = |F| \times |s| \times \cos(\theta)$$