Books usually use conservation of energy to solve problems in vertical circular motion. But, principle of conservation of energy for one particle is,
If all the $n$ forces $\vec F_i (i=1,2,3,..,n)$ acting on a particle are conservative, each with its corresponding potential energy $U_i(\vec r)$, the total mechanical energy, defined as $$E=\frac 12 mv^2 + \Sigma_i U_i(\vec r)$$ is constant in time.
but why are we not considering the centripetal force ( Tension, Normal reaction whatever that may be)? I don't understand this. Please help. How is this centripetal force taken into account?